An engineering graduate received a job offer with a promise of a seven percent a
ID: 2812603 • Letter: A
Question
An engineering graduate received a job offer with a promise of a seven percent annual raise in het salary She would like to accumulate two millin dollars in a retirement account by the time she retires from work ater35years. The ankmanagerest mates she can expect to receive a 5% nominal annual interest, compounded quarterly, throughout the 35 years. She is planning to make annual depasits to this account but wishes to make her first deposit at the end of the first year, with the lowest possible amount and increase it at the same 7% rate each year. Assuming once a year, end-of-year deposits showing all your calculations, determine how much her first deposit should be?Explanation / Answer
This is like an annuity cash flow stream for 35 years where the annual cash flow being deposited is increasing at 7% each year. The formula for the future value of growing annuity is :
FV = CF * [(1+r)t - (1+g)t] / (r-g) ; where CF is the first periodic payment, r is the applicable annual rate, g is the growth rate of annuity and t is the time period.
We are given : FV should be $2 million, t = 35 and g = 7%. The effective rate (r) = (1+5%/4)4 = 5.09%
Plugging in the values and solving for CF, we get:
2,000,000 = CF * [(1+5.09%)35 - (1+7%)35]/(5.09% - 7%)
CF = $ 7646.24
Hence her first deposit should be $7646.24