### 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

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