Question

Your beginning salary is $70,000. You deposit 12% at the end of each year in a savings account that earns 3% interest. Your salary increases by 2% per year. What value does your savings book show after 40 years?

Answer 1

Answer

It is given that Your beginning salary is $70,000. and you deposit 12% at the end of each year in a savings account.

In first year you will deposit 12% of 70,000 = 8400.

Also Your salary will increase by 2% per year and thus your deposit to saving will also increase by 2%.

Formula :

Future value of increasing periodic amount is given by :

FV = (P/(r - g))((1 + r)ⁿ - (1 + g)ⁿ)

where FV = Future value after n years that we have to calculate, P = Beginning amount = 8400 , r = interest rate = 3% = 0.03, g = growth rate of periodic deposits = 2% = 0.02 and n = time = 40

Hence FV = (P/(r - g))((1 + r)ⁿ - (1 + g)ⁿ) = (8400/(0.03 - 0.02))((1 + 0.03)⁴⁰ - (1 + 0.02)⁴⁰)

=> FV = 885358.43

Hence After 40 years your savings book will show $885358.43.