Question

You plan to invest $600 in your savings account this year and then you intend to increase the amount that you invest by 3% each year. If you invest in a savings account each that earns an effective annual interest rate of 7% how much money will you have in your account in 18 years?

Answer 1

Saving in Year 1 = $600
Growth Rate = 3%
Interest Rate = 7%
Time Period = 18 years

Saving in Year 2 = $600*1.03
Saving in Year 3 = $600*1.03^2
...
Saving in Year 18 = $600*1.03^17

Future Value = $600*1.07^17 + $600*1.03*1.07^16 + $600*1.03^2*1.07^15 + ... + $600*1.03^17
Future Value = $600 * 1.03^17 * [(1.07/1.03)^18 - 1] / [(1.07/1.03) - 1]
Future Value = $600 * [1.07^18 - 1.03^18] / 0.04
Future Value = $600 * 41.93748
Future Value = $25,162.49

So, you will have $25,162.49 in your account after 18 years.