Question

146 CHAPTER 4: EQUIVALENCE FOR REPEATED CASH FLOWS 4-93 A 25-year-old engineer is opening an individual retire- ment account (IRA) at a bank. Her goal is to accumu- late $1 million in the account by the time she retires from work in 40 years. The bank manager estimates she may expect to receive 8% nominal annual inter- est, compounded quarterly, throughout the 40 years. The engineer believes her income will increase at a 7% annual rate during her career. She wishes to start her IRA with as low a deposit as possible and increase it at a 7% rate each year. Assuming end-of-year deposits, how much should she deposit the first year?

Answer 1

Effective interest rate = (1 + i )^m - 1 = (1.02)^4 - 1 = 0.0824 = 8.24%

FV = $1000000

P for i = 8.24% and n = 40.

P = F(P/F, 8.24%, 40)

P = 1000000*(1 + 0.0824)^-40

P = 42120

Now we insert these values in P = A* [(1 - (1 + g)^n * (1 + i)^-n )/(i - g)]

P = A*[(1 - (1.07)^40 *(1.0824)^-40 )/(0.0824-0.0700)]

P = A* (29.78)

Now P = 42120, Hence,

First Deposit A = 42120/29.78 = 1414.37