# Future Value of a Single Sum of Money

Future value of a present single sum of money is the amount that will be obtained in future if the present single sum of money is invested on a given date at the given rate of interest. The future value is the sum of present value and the compound interest.

## Formula

The future value of a single sum of money is calculated by using the following formula.

 Future Value (FV) = Present Value (PV) × (1 + i)n

Where,
i is the interest rate per compounding period; and
n are the number of compounding periods.

## Examples

Example 1: An amount of $10,000 was invested on Jan 1, 2011 at annual interest rate of 8%. Calculate the value of the investment on Dec 31, 2013. Compounding is done on quarterly basis. Solution We have, Present Value PV =$10,000 Compounding Periods n = 3 × 4 = 12 Interest Rate i = 8%/4 = 2% Future Value FV = $10,000 × ( 1 + 2% )^12 =$10,000 × 1.02^12 ≈ $10,000 × 1.268242 ≈$12,682.42

Example 2: An amount of $25,000 was invested on Jan 1, 2010 at annual interest rate of 10.8% compounded on quarterly basis. On Jan 1, 2011 the terms or the agreement were changed such that compounding was to be done twice a month from Jan 1, 2011. The interest rate remained the same. Calculate the total value of investment on Dec 31, 2011. Solution The problem can be easily solved in two steps: STEP 1: Jan 1 - Dec 31, 2010 Present Value PV1 =$25,000 Compounding Periods n = 4 Interest Rate i = 10.8%/4 = 2.7% Future Value FV1 = $25,000 × ( 1 + 2.7% )^4 =$25,000 × 1.027^4 ≈ $25,000 × 1.112453 ≈$27,811.33

STEP 1: Jan 1 - Dec 31, 2011

Present Value PV2 = FV1 = $27,811.33 Compounding Periods n = 2 × 12 = 24 Interest Rate i = 10.8%/24 = 0.45% Future Value FV2 =$27,811.33 × ( 1 + 0.45% )^24 = $27,811.33 × 1.0045^24 ≈$27,811.33 × 1.113778 ≈ \$30.975.64

Written by Irfanullah Jan