You have just received an inheritance of 28 dollars comma 000 and would like to invest it into an account. The bank offers two investment plans, one for 4 years at 5 point 8 percent compounded annually and another for 3 years at 7 point 0 8 3 percent compounded annually. You want to make equal annual withdrawals from the account over the life time of the loan. Which investment will yield the highest annual withdraw and by what amount, given that the account will be zeroed out by the end of that period? Round your answer to the nearest cent.
Answer
A
3 year account; 8 dollars comma 281 point 8 8
B
4 year account; 10 dollars comma 436 point 3 4
C
4 year account; 8 dollars comma 043 point 5 9
D
3 year account; 10 dollars comma 685 point 6 3
Explanation
For equal annual withdrawals that reduce the account to zero, use the annuity payment formula: payment = 28,000 × r ÷ [1 − (1 + r)^(−n)]. The 4-year plan at 5.8% gives about $8,043.59 per year, while the 3-year plan at 7.083% gives about $10,685.63 per year. The 3-year account therefore yields the higher annual withdrawal: $10,685.63.
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