### Problem

If you wish to accumulate 140,000 in 3 years, how much must you invest today in an account that pays a nominal annual interest rate of 8% with six monthly compounding of interest?

### Solution

In this problem as the compounding is six monthly, a period is defined as being 6 months. All values need to be stated in relation to that period length. The term 3 years becomes 3 x 2 = 6 periods, and the annual discount rate 8% becomes a period discount rate of 8% / 2 = 4%.

The amount (PV) is invested now at the start of period 1, and is compounded forward for 6 periods (n) at a discount rate of 4% (i) and grows into a value of 140,000 (FV).

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

FV = 140,000 n = 6 i = 4% PV = FV /(1 + i)^{n}PV = 140,000 /(1 + 4%)^{6}PV = 110,644.03

### Explanation

The amount of 110,644.03 invested today in an account earning a nominal annual interest rate of 8% compounded every six months, will grow into an amount of 140,000 in 3 years time.

### PV3 Present Value Examples

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