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 1 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 savings at the end of 10 years?

d.     Would your answer change if the rate of interest on the second plan were 7 percent?

a)  FV = $14,139.84

b)     FV = $14,147.09

c)      Muffin should use the second plan

d) Yes. In this case, Muffin should use the first plan

Step-by-step explanation

a)     Because deposits are made semi - annually for 10 years, this qualifies to be an ordinary annuity whose future value would be given by;

FV = A * {(1 + r) ⁿ - 1}/ r

Where;

A-Periodic deposits/ savings, 500

r- Interest rate, 7/2 = 3.5%

n- Number of deposits, 10 * 2 = 20

FV = 500 * {(1.035) ²⁰ - 1}/ 0.035

     = 500 * 28.2797

     = $14,139.84

b)     FV = A * {(1 + r) ⁿ - 1}/ r

A=1,000, r = 7.5% and n = 10

FV = 1,000 * {(1.075) ¹⁰ - 1}/ 0.075

   = 1,000 * 14.1471

   = $14,147.09

c)      Muffin should use the second plan because it has a higher future or terminal value.

d)     Future value of the second plan when interest rate is 7%

FV = 1,000 * {(1.07) ¹⁰ - 1}/ 0.07

   = 1,000 * 13.8164

   = $13,816.45

Yes. In this case, Muffin should use the first plan because it has a higher future or terminal value compared to the second plan when interest rate is 7%.