# 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 Periodsn= 3 × 4 = 12 Interest Ratei= 8%/4 = 2% Future ValueFV= $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

PV= $25,000 Compounding Periods_{1}n= 4 Interest Ratei= 10.8%/4 = 2.7% Future ValueFV= $25,000 × ( 1 + 2.7% )^4 = $25,000 × 1.027^4 ≈ $25,000 × 1.112453 ≈ $27,811.33_{1}

STEP 1: Jan 1 - Dec 31, 2011

Present Value

PV= FV_{2}_{1}= $27,811.33 Compounding Periodsn= 2 × 12 = 24 Interest Ratei= 10.8%/24 = 0.45% Future ValueFV= $27,811.33 × ( 1 + 0.45% )^24 = $27,811.33 × 1.0045^24 ≈ $27,811.33 × 1.113778 ≈ $30.975.64_{2}

Written by Irfanullah Jan