# FV2 Future Value Example

### Problem

What will 100,000 grow to be in 9 years if it is deposited today in an account with a nominal annual interest rate of 6% with monthly compounding of interest?

### Solution

In this problem as the compounding is monthly, a period is defined as being one month. All values need to be stated in relation to that period length. The term 9 years becomes 9 x 12 = 108 periods, and the annual discount rate 6% becomes a period discount rate of 6% / 12 = 0.5%.

The amount of 100,000 (PV) is invested now at the start of period 1, and needs to be compounded forward 108 periods (n) to the end of period 108, at a discount rate of 0.5% (i).

This problem is solved using the future value of a lump sum formula as follows.

```PV = 100,000
n = 108
i = 0.5%

FV = PV x (1 + i)n
FV = 100,000 x (1 + 0.5%)108
FV = 171,369.95
```

### Explanation

The amount of 100,000 invested today in an account earning 8% compound interest, will grow in to an amount of 309,440.09 in 6 years time.

The amount of 100,000 invested today in an account earning a nominal annual interest rate of 6% compounded every month, will grow into an amount of 171,369.95 in 9 years time.

### FV2 Future Value Examples

This is one of many time value of money examples, discover another at the links below.