Question

Muffin Megabucks is considering two different savings plans. The first plan would have her deposit $500 every six months, and she would receive interest at a 7 percent annual rate, compounded semiannually. Under the second plan she would deposit $1,000 every year with a rate of interest of 7.5 percent, compounded annually. The initial deposit with Plan I would be made six months from now and, with Plan 2, one year hence. (a) What is the future (terminal) value of the first plan at the end of 10 years? (b) What is the future (terminal) value of the second plan at the end of 10 years? (c) Which plan should Muffin use, assuming that her only concern is with the value of her m) savings at the end of 10 years? (d) Would your answer change if the rate of interest on the second plan were 7 percent?

Answer 1

a. Future value of the first plan at the end of 10 years is calculated as =FV(rate,nper,pmt) in excel where rate = 0.07/2, nper = 10*2 = 20, pmt = 500

Future value of the first plan at the end of 10 years is calculated as =FV(0.07/2,20,500) = $14,139.84

b. Future value of the second plan at the end of 10 years is calculated as =FV(rate,nper,pmt) in excel where rate = 0.075, nper = 10, pmt = 1000

Future value of the second plan at the end of 10 years is calculated as =FV(0.075,10,1000) = $14,147.09

c. She should choose the second plan since the terminal value is higher than the first.

d. Yes, the answer will change if the interest on the second plan is only 7%. Because in this case, the terminal value of the second plan = =FV(0.07,10,1000) = 13,816.45 and hence the first plan becomes attractive.