### Problem

How many years will it take for 120,000 to grow to be 345,000 if it is invested in an account with an annual interest rate of 7%?

### Solution

The amount of 120,000 (PV) is invested now at the start of period 1, and needs to be compounded forward at a discount rate of 8% (i) to the value of 345,000 (FV).

This problem is solved using the lump sum number of periods formula as follows.

FV = 345,000 PV = 120,000 i = 7% n = LN (FV / PV) / LN (1 + i) n = LN (345,000 / 120,000) / LN (1 + 7%) n = 15.61

### Explanation

The amount of 120,000 invested today in an account earning 7% compound interest, will grow into an amount of 345,000 in 15.61 years time.

### NP1 Number of Periods Example

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

Last modified July 10th, 2019