Question

You have no retirement savings upon graduation from college, but you can afford to save $4,800 annually at the end of each year until retirement that you plan to take place 43 years from today. If you hope to have $800,000 in savings when you retire, what rate of return must you earn over that time? Goal: Years: Planned annual payment: 800,000 43 4,800.00 Required rate of return;

Answer 1

Future value required = $800,000 Term = 43 Years Annual savings = $4,800 Future value required = Annual savings * [( 1 + RR n - 11/RR $800.000 = $4,800 * [(1 + RR 43 -1 ]/RR $800.000 / $4,800 = [( 1+ RR 43 -1 ]/RR 166.666667 = [(1 + RR 43 -1 ]/RR [(1 +RR) 43 -1 ]/RR = 166.666667 To get required rate of return, we should go for trail and error appraoch... if required rate of return, RR = 5.57% L.H.S = [( 1+5.57%) 43 - 1]/5.57% = [10.285903 - 1]/0.0557 = 166.7128 = 166.7 (Rounded) = RH.S Therefore required rate = 5.57% Ans: 5.57% (Approximately)