Fact-checked by Grok 2 weeks ago

Discount rate

The discount rate is a key concept in finance and economics, referring primarily to either the interest rate charged by a central bank—such as the Federal Reserve in the United States—for short-term loans provided to commercial banks through its discount window, or the rate of return applied to discount future cash flows to their present value in investment valuation models like discounted cash flow (DCF) analysis, or the social discount rate used in cost-benefit analyses of public investments and policy decisions.^[1]^[2] In its monetary policy role, the discount rate serves as a tool for central banks to influence liquidity in the banking system and broader economic activity by setting the cost of borrowing reserves from the central bank, typically at a level above prevailing market rates to discourage routine use and promote stability.^[1] The Federal Reserve operates a tiered discount window with primary credit available to financially sound institutions at the lowest rate, secondary credit for those in weaker condition at a higher penalty rate, and seasonal credit for smaller banks with predictable cash flow fluctuations.^[1] These loans are usually overnight and fully collateralized, but can extend longer during financial stress, as seen when borrowing surged to approximately $111 billion in October 2008 amid the global financial crisis.^[3] Adjustments to the rate, such as the primary rate cut from 6.25% to 5.75% in August 2007, signal policy shifts to ease or tighten credit conditions.^[1] In financial valuation, the discount rate represents the expected rate of return or opportunity cost of capital, accounting for the time value of money and investment risk, and is often calculated as the weighted average cost of capital (WACC) for corporate projects or the risk-free rate plus a risk premium for specific analyses.^[2] It is essential in DCF models to determine whether an investment's projected cash flows justify its upfront cost, using formulas like the present value (PV) = future value (FV) / (1 + discount rate)^n, where n is the number of periods.^[1] For example, discounting $100 in annual cash flows over seven years at a 5% rate yields a net present value (NPV) of approximately $578.64, compared to $700 without discounting, highlighting how higher rates reduce the appeal of long-term or risky projects.^[2] Common applications include corporate budgeting, where a hurdle rate exceeds the WACC to ensure value creation, and bond pricing, where it aligns with the cost of debt.^[2]

Definition and Fundamentals

Core Concept

The discount rate is the interest rate used to adjust the value of future cash flows or benefits to their equivalent present value, reflecting the time value of money.^[4] This adjustment accounts for the fundamental principle that money available today holds greater worth than the same amount in the future, as it can be invested immediately to generate returns.^[5] A primary reason for this valuation difference lies in opportunity cost, where funds held now enable earning interest or alternative investments, whereas deferred funds miss such potential gains.^[5] Future sums also involve inherent risks, such as uncertainty in receipt or economic changes, which diminish their perceived value and necessitate discounting to incorporate these factors.^[5] Additionally, inflation plays a role by eroding purchasing power over time, reinforcing why present money is preferable.^[5] Discount rates are distinguished as nominal or real, with nominal rates embedding expected inflation to reflect observed market conditions, while real rates exclude inflation to capture genuine changes in economic value.^[6] The selection between them hinges on the nature of the cash flows analyzed: nominal rates pair with inflation-adjusted figures, whereas real rates align with constant-dollar estimates, ensuring analytical consistency.^[6] Inflation influences this choice by increasing nominal rates, as it compensates for the diminished future buying power of money.^[6] The concept traces its origins to 18th-century finance, emerging prominently in the valuation of annuities amid growing interest in life contingencies.^[7] Richard Price, a British nonconformist minister and Fellow of the Royal Society, advanced these ideas in his 1771 work Observations on Reversionary Payments, where he employed discounting to assess annuity values based on mortality statistics from London's Bills of Mortality.^[7] Price's contributions critiqued prevailing annuity schemes and laid groundwork for actuarial practices, influencing the systematic application of discount rates in financial and insurance contexts.^[7]

Key Components

The selection of a discount rate is shaped by several interrelated factors that reflect economic realities and investor behavior, including the risk premium, liquidity preference, and inflation expectations. The risk premium compensates investors for the uncertainty and potential variability in future cash flows, adding to the baseline rate to account for non-diversifiable risks.^[8] Liquidity preference, rooted in the demand for readily convertible assets, introduces a premium that rewards holding less liquid investments, as investors require higher returns to forgo the flexibility of cash or equivalents.^[8] Inflation expectations further adjust the rate, incorporating anticipated erosion of purchasing power; according to the Fisher equation, the nominal discount rate approximates the real rate plus expected inflation, ensuring future values are deflated appropriately.^[9] A foundational element is the pure time preference rate, which captures the non-monetary impatience for current consumption over future utility, independent of economic growth or risk. This rate, often denoted in economic models as the utility discount factor, arises from individuals' inherent valuation of present well-being, influencing long-term discounting in both personal and social contexts.^[10] In the Ramsey framework, it forms the core of the real discount rate, representing ethical or psychological bias toward the present without monetary distortions.^[11] The opportunity cost serves as the baseline for the discount rate, embodying the foregone return from the next best alternative investment, typically benchmarked against low-risk assets like government bonds. For instance, U.S. Treasury yields often proxy the risk-free component, providing a floor rate reflective of time value without default risk.^[12] Adjusted rates for uncertainty diverge from this risk-free benchmark by incorporating premiums for specific hazards, such as market volatility or project-specific risks, ensuring the rate aligns with the investment's profile rather than a generic safe-haven yield.^[8] These components collectively determine the rate's magnitude, underpinning its application in present value assessments.^[13]

Financial Applications

Discounted Cash Flow Analysis

Discounted cash flow (DCF) analysis is a valuation method used to estimate the value of an investment based on its expected future cash flows, adjusted to their present value using a discount rate that reflects the time value of money and risk.^[14] This approach is fundamental in corporate finance for assessing projects, companies, or assets by projecting cash inflows and outflows over a forecast period and discounting them back to today.^[15] The process begins with projecting future cash flows, typically free cash flow to the firm (FCFF) or to equity (FCFE), based on historical financial data, industry trends, and management forecasts. For FCFF, this involves starting from earnings before interest and taxes (EBIT), adjusting for taxes, adding non-cash charges, and subtracting reinvestments in working capital and fixed assets. These projections are made for a high-growth period, often 5 to 10 years, followed by a terminal value assuming stable growth thereafter. The next step is to discount these cash flows using an appropriate rate: for firm-level valuation, each period's FCFF is divided by (1 + discount rate) raised to the power of the period number, and the terminal value is similarly discounted from the end of the forecast period. The sum of these present values yields the total value.^[14]^[15] Selecting the discount rate is critical, as it represents the opportunity cost of capital and the risk-adjusted required return. In DCF for firms, the weighted average cost of capital (WACC) is commonly used, calculated as the weighted average of the after-tax cost of debt and the cost of equity, with weights based on market values of debt and equity. The cost of equity is often estimated via the Capital Asset Pricing Model (CAPM) as the risk-free rate plus beta times the equity risk premium, while the cost of debt incorporates the risk-free rate plus a default spread, adjusted for taxes. This ensures the rate matches the cash flows being discounted—WACC for FCFF to avoid circularity in financing assumptions.^[14]^[15] Consider a simple example of valuing a project with expected cash flows of $100 at the end of year 1 and $200 at the end of year 2, using a 5% discount rate. The present value of the year 1 cash flow is calculated as $100 / (1 + 0.05)^1 = $95.24. For year 2, it is $200 / (1 + 0.05)^2 = $181.41. Summing these gives a total present value of $276.65, representing the project's worth today. This illustrates how discounting reduces the value of future amounts due to time and risk.^[15] Sensitivity analysis examines how variations in the discount rate affect the overall valuation, highlighting the model's robustness to key assumptions. For instance, increasing the rate from 5% to 7% in the above example reduces the present value to $93.46 for year 1 and $174.69 for year 2, totaling $268.15—a decrease of about 3% that underscores the inverse relationship between discount rates and valuations. Analysts often test ranges around base-case rates (e.g., ±1-2%) alongside other inputs like growth rates to identify scenarios where the investment remains viable, aiding decision-making under uncertainty.^[14]^[15]

Net Present Value Calculation

Net Present Value (NPV) is a financial metric that represents the difference between the present value of cash inflows and the present value of cash outflows over a period of time, effectively measuring the profitability of an investment or project by accounting for the time value of money. It is computed as the initial investment subtracted from the sum of the discounted future cash flows.^[16]^[17] The standard formula for NPV is:

\text{NPV} = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t}

where C_0 is the initial investment (outflow), C_t is the net cash flow at time t, r is the discount rate, and n is the number of periods.^[18]^[19] The primary decision rule in capital budgeting using NPV is to accept projects with a positive NPV, indicating that the investment is expected to generate returns exceeding the cost of capital, and to reject those with a negative NPV, as they would destroy value. Projects with zero NPV are typically considered indifferent, though they may be accepted if they align with strategic goals.^[20]^[21] To illustrate, consider a project requiring an initial outlay of $500, with expected cash inflows of $300 at the end of year 1 and $400 at the end of year 2, discounted at a 10% rate. The present value of the year 1 inflow is \frac{300}{1.10} \approx 272.73, and the year 2 inflow is \frac{400}{1.10^2} \approx 330.58. Summing these gives a total present value of approximately $603.31, resulting in an NPV of $603.31 - $500 \approx $103, suggesting the project should be accepted.^[22]^[23] NPV models readily accommodate uneven cash flows by applying the discounting formula to each individual cash flow based on its specific timing, rather than assuming uniform annuities. For longer-term projects, adjustments often include estimating a terminal value to capture cash flows beyond the explicit forecast horizon; this value, typically calculated as a perpetuity (e.g., final year's cash flow growing at a perpetual rate divided by the difference between the discount rate and growth rate), is discounted back to the present and added to the final period's cash flow.^[18]

Economic and Policy Uses

The social discount rate (SDR) is the interest rate applied in cost-benefit analyses of public projects to evaluate the present value of future societal costs and benefits, reflecting society's collective valuation of intergenerational welfare rather than private market returns.^[24] Unlike market-based rates, which may exceed 5-7%, the SDR is typically set lower, often in the range of 1-3% for long-term environmental or social initiatives, to ensure that benefits accruing to future generations are not unduly diminished.^[25] This rate incorporates elements such as the pure rate of time preference, which captures society's ethical stance on favoring present over future utility.^[24] A key debate surrounds the appropriate level and structure of the SDR, particularly whether it should decline over time to account for expected economic growth and uncertainty in long-term projections. Proponents of declining rates argue that as per capita income rises, future generations' ability to afford benefits increases, justifying lower discounting for distant horizons; for instance, the UK's Treasury adopted a declining schedule in 2003, starting at 3.5% and tapering to 1% beyond 300 years.^[25] In June 2025, HM Treasury commissioned an independent review of the Green Book's discount rate methodology to reassess its application to long-term public investments.^[26] In contrast, the 2006 Stern Review on climate change advocated a near-constant low rate of 1.4%, emphasizing minimal time preference to prioritize urgent mitigation, which sparked criticism for potentially overvaluing distant risks compared to higher rates like the UK's 3.5%.^[27]^[11] The SDR finds prominent applications in evaluating long-term public investments, such as climate change mitigation, where low rates amplify the present value of avoided future damages; for example, the U.S. Environmental Protection Agency's social cost of carbon estimates rely on SDRs around 2-3% to assess policy impacts over centuries.^[28] In infrastructure planning, governments use the SDR to appraise projects like transportation networks or dams, ensuring societal benefits like reduced congestion or flood protection are weighed against upfront costs over decades.^[24] Similarly, in public health interventions, such as vaccination programs or pollution controls, the SDR helps quantify the value of averted morbidity and mortality in future populations, as seen in analyses of climate-related health burdens.^[29] Ethical considerations underpin the SDR's design, centering on intergenerational equity—the principle that current generations should not impose undue burdens on successors by excessively discounting their welfare. High rates risk over-discounting future benefits, potentially justifying inaction on issues like environmental degradation that disproportionately affect the unborn, whereas lower rates promote fairness by treating future lives as comparably valuable to present ones.^[30] This tension highlights the SDR's role not just as a technical tool but as a mechanism for embedding moral judgments about sustainability and justice across time horizons.^[31]

Central Bank Discount Rates

The central bank discount rate serves as a key instrument in monetary policy, representing the interest rate at which eligible depository institutions can borrow funds, typically on a short-term basis, directly from the central bank to meet reserve requirements or manage liquidity needs. This mechanism, often referred to as the discount window in the United States, provides a safety valve for banks facing temporary funding shortages, thereby supporting financial stability and preventing broader disruptions in the banking system. By adjusting the discount rate, central banks signal their policy intentions—raising it to tighten credit conditions and curb inflation, or lowering it to encourage lending and stimulate economic activity. For instance, the Federal Reserve sets three types of discount rates: primary credit for financially sound institutions, secondary credit for those with weaker conditions, and seasonal credit for smaller institutions with predictable fluctuations, with the primary credit rate serving as the benchmark for policy signaling.^[32]^[33] In practice, the discount rate influences the broader economy by anchoring interbank lending rates and affecting the availability of credit to businesses and consumers. When central banks raise the discount rate, it increases the cost of borrowing from the central bank, which in turn pressures commercial banks to raise their own lending rates, reducing money supply and dampening inflationary pressures. Conversely, a lower rate facilitates easier access to funds, promoting investment and growth. This rate also shapes overall interest rate expectations, as it sets a ceiling for overnight borrowing costs in the interbank market, thereby guiding market rates like the federal funds rate. The impact extends to credit availability, where higher discount rates can constrain bank lending, slowing economic expansion, while lower rates enhance liquidity and support recovery efforts.^[34]^[35] A notable historical example is the U.S. Federal Reserve's aggressive discount rate hikes from 2022 to 2023 in response to surging inflation, which peaked at 9.1% in June 2022. Starting from a primary credit rate of 0.25% in early 2022, the Fed incrementally increased it through multiple adjustments, reaching 5.50% effective July 27, 2023, to align with its federal funds target range of 5.25–5.50% and combat post-pandemic inflationary pressures driven by supply chain disruptions and fiscal stimulus. These hikes, part of 11 total federal funds rate increases totaling 525 basis points, successfully moderated inflation, bringing the Consumer Price Index to around 3% by mid-2023, though they also contributed to tighter credit conditions and slower growth. Subsequently, as inflation eased further toward the 2% target, the Federal Reserve implemented rate cuts, reducing the primary credit rate in steps from 5.50% to 4.00% as of October 30, 2025.^[36]^[37]^[38]^[39] Distinct from the federal funds rate, which is the target rate for unsecured overnight loans between banks in the interbank market, the discount rate functions primarily as a penalty rate for emergency borrowing from the central bank, set equal to the top of the FOMC's target range for the federal funds rate (a spread of 0 basis points since March 2020), serving as a reliable backstop without a built-in penalty, while administrative stigma and other factors discourage routine reliance and promote market-based funding.^[32] This ensures the discount window remains a backstop rather than a primary funding source, preserving the federal funds rate's role in transmitting monetary policy through open market operations. While the federal funds rate directly influences short-term market rates, the discount rate reinforces policy by providing a predictable upper bound, with usage spiking during stress periods like the 2008 financial crisis or the 2023 banking turmoil.^[40]

Mathematical Formulation

Discrete Discounting

Discrete discounting refers to the process of calculating the present value of future cash flows by applying a discount rate over discrete time periods, such as years or quarters, which is fundamental in financial modeling where compounding occurs at fixed intervals.^[41] The core formula for the present value (PV) of a single future value (FV) is given by:

PV = \frac{FV}{(1 + r)^n}

where r is the discount rate per period and n is the number of periods.^[41] This formula arises directly from the principles of compound interest, where the future value grows as FV = PV \times (1 + r)^n; inverting this equation yields the discounting relationship, reflecting the geometric progression of value over time as each period's interest compounds multiplicatively on the previous amount.^[41] For illustration, consider a future value of $100 discounted at an annual rate of 5% over 3 years: PV = 100 / (1.05)^3 \approx 86.38, demonstrating how the time value of money reduces the current worth of deferred payments.^[41] In discrete models, multiple periods are handled by applying the formula iteratively for each cash flow, while annuities—regular periodic payments—simplify to a closed-form expression derived from the sum of a geometric series. The present value of an annuity-immediate of payment PMT per period for n periods is:

PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}

This sums the discounted values of each payment, where the first occurs at the end of the first period.^[42] For example, annual payments of $100 for 5 years at 9% yield PV \approx 388.97, underscoring the role of discrete discounting in valuing streams like loan repayments or investment returns.^[42]

Continuous Discounting

Continuous discounting models the present value of future cash flows using a smooth exponential function, treating time as a continuum rather than discrete intervals, which is particularly useful in advanced theoretical frameworks such as stochastic processes and optimal control problems. This approach assumes infinitely frequent adjustments, leading to a more precise representation of time value in models where events occur continuously.^[43] The core formula for the present value under continuous discounting is

PV = FV \cdot e^{-rt},

where PV is the present value, FV is the future value, e is the base of the natural logarithm (approximately 2.718), r is the continuous discount rate, and t is the time horizon in years. This equation inverts the continuous compounding growth formula FV = PV \cdot e^{rt}, applying the discount factor e^{-rt} to reflect the time value of money.^[44]^[45] This continuous form derives from the discrete discounting formula as the compounding frequency increases indefinitely. Starting with the discrete present value PV = FV / (1 + r/m)^{mt}, where m is the number of compounding periods per year, taking the limit as m \to \infty yields (1 + r/m)^{m} \to e^{r}, resulting in the exponential discount PV = FV \cdot e^{-rt}. This limit captures the idealized case of instantaneous reinvestment, maximizing the mathematical elegance for differential equation-based analyses.^[46]^[44] In financial derivatives pricing, continuous discounting underpins the Black-Scholes model, which values European options by incorporating the present value of the strike price as K e^{-rt} within its partial differential equation framework, assuming constant risk-free rate and continuous trading. The original formulation relies on this exponential discounting to hedge risks dynamically in a continuous-time geometric Brownian motion setting.^[47]^[48] In macroeconomic theory, the Ramsey growth model uses continuous discounting in the intertemporal utility function \int_0^\infty e^{-\rho t} u(c(t)) \, dt, where \rho is the rate of time preference, to derive optimal consumption and saving paths that maximize welfare over infinite horizons. This setup, introduced in continuous time via differential equations, balances current utility against future growth.^[49]^[50] A key distinction in effective rates arises when comparing continuous to discrete compounding: a continuous rate of 5% yields an effective annual return of e^{0.05} - 1 \approx 5.13\%, equivalent to a discrete annually compounded rate of approximately 5.13%, highlighting the marginal advantage of continuous processes over annual discretization for the same nominal rate.^[44]

References

[1]
Understanding the Discount Rate: Fed's Tool and DCF Analysis ...
The discount rate is the lending rate at the Federal Reserve's discount window, where banks can get a loan if they can't secure funding from another bank on the ...Understanding the Fed's... · Fed's Discount Rate · Example
[2]
Discount Rate - Definition, Types and Examples, Issues
A discount rate is the rate of return used to discount future cash flows back to their present value.
[3]
Discounting 101 - Resources for the Future
Jan 16, 2020 · Discounting is the process of converting a value received in a future time period to an equivalent value received immediately.Why Discount? · Setting the Discount Rate · Discounting and Climate...
[4]
Time Value of Money (TVM): A Primer - HBS Online
Jun 16, 2022 · The time value of money (TVM) is a core financial principle that states a sum of money is worth more now than in the future.
[5]
The Mechanics of Discounting
Discounting is the reverse of compounding. We reduce a future value to a present value by discounting. Discounting is an important concept for CBA.
[6]
[PDF] 225 the early history of the annuity - Casualty Actuarial Society
During the same year in London, the London. Annuity Society was founded and in 1776, the Laudable Society of Annuitants, was established. Dr. Richard Price, a ...
[7]
Interest Rates and Time Value of Money – CFA Level I - PrepNuggets
Interest rates consist of the real risk-free rate, inflation premium, maturity risk premium, liquidity premium, and default risk premium.
[8]
Fisher Equation - Overview, Formula and Example
The equation states that the nominal interest rate is equal to the sum of the real interest rate plus inflation. The Fisher equation is often used in situations ...
[9]
Changing the Discount Rate by Adjusting the Pure Rate of Time ...
Jun 25, 2023 · Hence the discount rate depends on time preference through the marginal utility term. We derive an analytical expression of this relationship ...
[10]
A Formula For Success: Reviewing The Social Discount Rate - Oxera
Sep 30, 2020 · The rate of pure time preference (δ) represents the relative weight that is placed on the welfare of people alive now versus people alive in the future.
[11]
Discount Rate | Formula + Calculator - Wall Street Prep
Discount Rate is the minimum rate of return expected to be earned on an investment given its specific risk profile.How to Calculate Discount Rate · Full-Form Discount Rate: What...
[12]
Discount Rate: Full Explanation and Excel Examples
The discount rate represents expected annualized returns on an investment, cost of capital for companies, and opportunity cost for investors.
[13]
https://breakingintowallstreet.com/kb/finance/discount-rate/
[14]
[PDF] Discounted Cash Flow Valuation - NYU Stern
I The next step in the process is deciding. • which cash flow to discount, which should indicate. • which discount rate needs to be estimated and. • what ...
[15]
Net Present Value (NPV) - Corporate Finance Institute
Net Present Value (NPV) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present.
[16]
Net Present Value (NPV) | Formula + Calculator - Wall Street Prep
The discount rate, date, and cash flow assumptions for calculating the net present value are listed below: Discount Rate = 10%; Year 0 (8/31/21) = -$100m; Year ...Npv Formula · Npv Calculator -- Excel... · 1. Capital Budgeting Project...Missing: 500 300 400
[17]
NPV Formula - Learn How Net Present Value Really Works, Examples
Additionally, a terminal value is calculated at the end of the forecast period. Each of the cash flows in the forecast and terminal value is then discounted ...What is the NPV Formula? · What is the Math Behind the...
[18]
Investment Decisions and Capital Budgeting - Duke People
Jan 5, 1997 · The net present value (NPV) of a project is defined as the present value of all future cash flows produced by an investment, less the initial ...
[19]
[PDF] CHAPTER 5 NET PRESENT VALUE AND OTHER INVESTMENT ...
The decision rule is to accept projects that have a positive NPV, and reject projects with a negative NPV. NPV is superior to the other methods of analysis.
[20]
[PDF] Net Present Value and Payback Period: An Analysis
Dec 7, 2023 · The decision criteria for Net present value is to accept if NPV ≥ 0 and decline if NPV < 0. In contrast to Payback Period, Net Present Value ...
[21]
Net Present Value (NPV): What It Means and Steps to Calculate It
Net present value (NPV) tells you if the money an investment makes in the future is worth more or less than what it costs today.Disadvantages of Net Present... · Time Value of Money · Microsoft Excel
[22]
Net Present Value (NPV) Calculator - CalculateStuff.com
In order to calculate NPV, we must discount each future cash flow in order to get the present value of each cash flow, and then we sum those present values ...
[23]
The Social Discount Rate: A Primer for Policymakers | Mercatus Center
Jun 30, 2020 · The social discount rate used in cost-benefit analysis (CBA) is an interest rate applied to benefits and costs that are expected to occur in ...
[24]
What are social discount rates? - Grantham Research Institute ... - LSE
May 1, 2018 · Social discount rates (SDRs) are used to put a present value on costs and benefits that will occur at a later date.
[25]
The obscure calculation transforming climate policy
Dec 6, 2022 · Stern used a very low discount rate, 1.4 percent, to support the conclusion that large investments were urgently needed to prevent future ...
[26]
Social Cost of Carbon 101 - Resources for the Future
Discounting 101. How does discounting help decisionmakers understand the costs and benefits of choices and policies—and how does it apply to climate change?
[27]
[PDF] Public Health Consequences and Cost of Climate Change Impacts ...
Table 4-6 provides the discounting factors when using a social discount rate of 3 percent or 7 percent. The public health cost calculations presented in ...
[28]
[PDF] Intergenerational equity and the social discount rate - AgEcon Search
Intergenerational equity-adjusted social discount rates are derived as a means of decomposing the intergenerational equity aspect of the social discount rate.<|separator|>
[29]
[PDF] Intergenerational equity and social discount rates - PhilArchive
Nov 28, 2016 · Others argued that moral issues should be somehow disentangled from the practice of discounting (Sunstein and Rowell, 2007, p. 199), and ...
[30]
Discount Window - Federal Reserve Board
May 20, 2024 · The discount window allows depository institutions and US branches and agencies of foreign banks to borrow from Federal Reserve Banks after executing legal ...General Overview · 1. Primary Credit · Collateral Valuation And...
[31]
The Discount Window
Jul 6, 2024 · Federal Reserve lending to depository institutions (the “Discount Window”) plays an important role in supporting the liquidity and stability of the banking ...
[32]
The Fed's Discount Window: Who, What, When, Where and Why?
Apr 16, 2025 · The discount window is a way the Federal Reserve can lend money to financial institutions, including commercial banks, thrifts and credit unions.
[33]
Why Do Central Banks Have Discount Windows?
Mar 30, 2011 · The discount window plays a key role in supporting Federal Reserve open market operations and the implementation of monetary policy.<|control11|><|separator|>
[34]
Implementation Note issued July 26, 2023 - Federal Reserve Board
Jul 26, 2023 · ... primary credit rate to 5.5 percent, effective July 27, 2023. In taking this action, the Board approved requests to establish that rate ...
[35]
[PDF] Minutes of the Board's discount rate meetings from July 17 and July ...
Jul 26, 2023 · Louis, Minneapolis, and San Francisco had voted on July 13, 2023, to establish a primary credit rate of 5.50 percent (an increase from 5.25 ...
[36]
Historical U.S. Inflation Rate by Year: 1929 to 2025 - Investopedia
In 2022, inflation reached some of the highest levels seen since 1981, hitting 9.1% in the wake of the COVID-19 pandemic.What Is the Inflation Rate? · What Is the Current Inflation... · Rates From 1929-2025
[37]
[PDF] The Discount Window - Instruments of the Money Market
The discount window refers to lending by each of the 12 regional Federal Reserve Banks to depository institutions. Discount window loans generally fund only ...
[38]
None
### Summary of Financial Analysis Concepts from Chapter 2
[39]
[PDF] Chapter 2 Annuities - Financial Mathematics for Actuaries
The present value of an annuity is the sum of the present values of each payment. Example 2.1: Calculate the present value of an annuity-immediate of amount ...Missing: discrete | Show results with:discrete
[40]
Continuous Compounding Definition and Formula - Investopedia
Continuous compounding is the point at which compound interest reaches its maximum potential, being calculated and added to an account's balance without limit.
[41]
Understanding Continuous Compound Interest - Investopedia
The formula for continuous compounding is simpler than for discrete compounding intervals. ... PV = F e − r c n = ( $ 1 0 0 ) e − ( 0 . 0 6 ) ( 3 ) = $ 1 0 ...Missing: rt} | Show results with:rt}
[42]
1.7 Continuous compounding - Financial Mathematics - Fiveable
Represents current worth of future cash flow or payment · Calculated using formula P V = F V e − r t PV = FV e^{-rt} PV=FVe−rt in continuous compounding ...
[43]
Discrete Compounding vs. Continuous Compounding - Investopedia
To calculate continuous compounding for an interest-generating contract, the formula needs to be written as: F V = P × e r t FV=P\times e^{rt} FV=P×ert.
[44]
Black-Scholes Model: What It Is, How It Works, and Options Formula
The Black-Scholes call option formula is calculated by multiplying the stock price by the cumulative standard normal probability distribution function.
[45]
[PDF] Fischer Black and Myron Scholes Source: The Journal of Political Eco
Author(s): Fischer Black and Myron Scholes. Source: The Journal of Political Economy, Vol. 81, No. 3 (May - Jun., 1973), pp. 637-654. Published by: The ...
[46]
[PDF] A Mathematical Theory of Saving Author(s): F. P. Ramsey Source
Let us suppose first that the rate of discount for utility p is less than the rate of interest r. Then equations (1) and (2) are unchanged, but equation (3).Missing: continuous | Show results with:continuous
[47]
Ramsey and Intergenerational Welfare Economics
Jun 1, 2019 · Ramsey also assumed, probably because the mathematics is simpler, that time is a continuous variable, not discrete. Let $t \ge 0$ denote time.Missing: original | Show results with:original