# Discount Rate Calculator

Created by Tibor Pál, PhD candidate
Reviewed by Arturo Barrantes and Adena Benn
Based on research by
Cipra, T. Financial and Insurance Formulas (2010)
Last updated: Feb 02, 2023

We created this discount rate calculator to help you estimate the discount rate of a given flow of payments. More specifically, you can compute either the discount rate of a given present and future value or calculate some discount rates with an additional payment flow, such as an annuity.

Read further and learn the following:

• What is the discount rate definition?
• What is the discount rate formula?
• How to calculate the discount rate?

To calculate the present value by the discount rate, you may want to check our present value calculator.

## What is the discount rate definition?

The discount rate is the interest rate applied in discounted cash flow (DCF) analysis to determine the present value of future cash flow. The discount rate is an essential base of comparison since it indicates the profitability of an investment or project. Profit may arise when the discount rate exceeds the interest rate (i.e., cost of borrowing) on capital required for carrying out the investment.

## Federal funds rate vs discount rate

Note that discount rate may refer to another concept: the interest rate charged on discount loans (short-term funds) by the central bank to commercial banks. With this tool, monetary policy can eventually affect loan activity, economic output, and inflation. For example, the central bank may raise the discount rate when inflation expectation is high.

## How to calculate discount rate - the discount rate formula

When you wish to compute the discount rate with two cash flows (i.e., present value and future value), you can apply the following discount rate formula.

$\small DR = \bigg(\frac{FV}{PV}\bigg)^{\frac{1}{i\times m}} - 1$

Where:

• $DR$ is the discount rate;
• $PV$ stands for Present Value;
• $FV$ is the Future Value;
• $i$ is the number of periods (years), and
• $m$ is the compounding frequency in the given period (year).

Note that the resulting rate is the periodic discount rate, which is identical to the annual discount rate when compounding occurs once a year.

To get more insight into the computational way of the discount rate with periodic cash flows, check our rate of return calculator (with identical cash flows) or IRR calculator (with various cash flows).

## How do I use the discount rate calculator?

Follow the below steps for estimating the discount rate.

1. Main specification
• Present Value (PV) - The principal amount at the beginning of the investment or project. It can be considered the first cash flow.

• Future Value (PV) - The principal amount at the end of the investment or project. It can be considered the last cash flow in the given interval.

• Term or number of periods - the interval between the first and the last cash flow set by the present and the future values.

• Compounding frequency (m) - the number of times interest compounding occurs in one year or a period. You can choose one of the following compounding frequencies, where the fraction in the brackets corresponds to the occurrence of compounding in a given period.

• Yearly (1/Yr);
• Semi-annually (2/Yr);
• Quarterly (4/Yr);
• Monthly (12/Yr);
• Weekly (52/Yr);
• Daily (365/Yr); or
• Continuous (∞).

Note that the periodic discount rate is associated with the rate computed to a given compounding period (i.e., if the compounding frequency is monthly, the periodic discount rate of a 12 percent discount rate is 1 percent).

1. Periodic cash flows
• Cash Flow (CF) - the amount of money paid (invested) or withdrawn (realized) in a given period.

• Cash flow frequency - the regularity of the above cash flow.

• Types of cash flow - the cash flow may occur at the beginning or the end of the given period.

After setting all these variables, you will immediately see the estimated discount rate with complementary details (if applicable), such as the periodic discount rate or total cash flow.

## FAQ

### How to find the discount rate?

To find the discount rate for investment with present and future value, you need to take the following steps:

1. Divide the future value by the present value, FV/PV.'
2. Raise the value to the power of one divided by the product of periods and the compounding frequency, (FV/PV)^(1/(i×m)).
3. Deduct one from the resulting value. This is the periodic discount rate, (FV/PV)^(1/(i×m)) - 1.

### What is the discount rate of a $1,000 ten-years annuity with$2,000 future value?

The discount rate of a $1,000 ten-year annuity with a $2,000 future value with monthly compounding frequency is 6.952% annually or 0.579% monthly.

### Can the discount rate be negative?

Yes. If the present value of an investment or liability is higher today than at a future date, the discount rate becomes negative. The negative discount rate may suggest that a given investment is not profitable.

Tibor Pál, PhD candidate
Main specifications
Present Value (PV)
$Future Value (FV)$
Term or number of periods
yrs
Compounding frequency
Yearly (1/Yr)
Periodic cash flows
Cash Flow (CF)
\$
Cash flow frequency
Yearly
Type of cash flows
End of period
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