# How to Calculate the Unknown Interest Rate for a Present Value

by David Rodeck ; Updated September 11, 2015According to the time value of money, it is better to receive a dollar in the present versus a dollar in the future. This is because a dollar in the present will grow to be more than a dollar at a future date due to inflation and investment returns. This total growth rate is the interest rate of an investment. The unknown interest rate of an investment can be calculated if its initial present value, expected future value and years of investment are given. This can be done on a financial calculator or by hand.

## Using a Financial Calculator

Find the initial investment present value. Input this amount as PV on your financial calculator. Make sure to enter the PV as a negative value so the calculator knows its a cash outflow.

Find the investment's final value. Input the final value as FV on your calculator. This will be a positive number as it is a cash inflow to the investor.

Find the total years of investment. Input the number of years as "N" on the calculator.

Hit the interest button on your calculator for it to compute the unknown interest rate. Example: An investment costs $2,000 initially and will return $5,000 in 10 years. What is the interest rate? Input PV = -2,000 FV = 5,000 N = 10 CPT r = 9.60 percent per year

## Manual Calculation

Find the initial investment, final investment return and total years of investment for the unknown interest rate.

Rearrange the PV formula so that the unknown is r. The PV formula is PV = FV(1+r)^y. This can be rearranged to r = (FV/PV)^(1/y) - 1

Input the known variables in the formula and solve for r. Example: An investment costs $2,000 initially and will return $5,000 in 10 years. What is the interest rate? r = (FV/PV)^(1/y) - 1 = (5000/2000)^(1/10) - 1 = 2.5^0.1 - 1 = 1.096 - 1 = 0.096 = 9.6 percent

#### References

- Moneychimp: Present Value/Rate of Return
- "Financial Planning: Process and Environment" Craig Lemoine, et al.; 2009

#### Photo Credits

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