Question 7-8 A 25-year old engineer is opening an individual retirement account

Question

Question 7-8 A 25-year old engineer is opening an individual retirement account (RRSP) at a bank. Her goal is to accumulate $1 million in the account by the time she retires in 40 years. The bank manager estimates she may expect to receive 8% nominal annual interest, 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 with as low a deposit as possible to her RRSP now and increase it at a 7% rate each year. Assuming end of year deposits, determine the amount she should deposit the first year. This amount is close to O $1414 O $1212 O $1616 O $1010

Explanation / Answer

This amount is close to $1414

Since there are annual deposits, but quarterly compounding, we must first compute the effective interest rate per year.

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

F = $1,000,000

P for i = 8.24% and n = 40.

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

= $1,000,000 (1 + 0.0824)-40

= $42,120

Now we insert these values in P = A 1 [(1 - (1 + g) n (1 + i)-n )/(i - g)] $42,120

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

= A 1 (29.78)

The first RRSP deposit,

A 1 = $42,120/29.78 = $1,414

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