Question

Suppose you want to have $300,000 for retirement in 30 years. Your account earns 5% interest. a) How much would you need to deposit in the account each month? $ b) How much interest will you earn?

Answer 1

Amount needed at retirement FV = $300000

time period t = 30 years

interest rate r = 5% compounded monthly

So, ,monthly deposits is calculated using FV formula of annuity

PMT = FV*(r/n)/((1+r/n)^(n*t) - 1) = 300000*(0.05/12)/((1 + 0.05/12)^(12*30) - 1 ) = $360.46

So, monthly deposits = $360.46

Total amount deposited = monthly deposit*number of payment = 360.46*12*30 = $129767.35

So, interest portion = final value - total mount deposited = 300000 - 129767.35 = $170232.65