Question 10 • CARE_24_25_TX-Mathematical Models with Applications B
You have just received an inheritance of $28,000 and would like to invest it into an account. The bank offers two investment plans, one for 4 years at 5.8% compounded annually and another for 3 years at 7.083% 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 return over the duration of the loan, given that the account will be zeroed out by the end of that period?
Answer
A
3 year account; $32,056.89
B
4 year account; $42,742.52
C
3 year account; $24,130.77
D
4 year account; $32,174.36
Explanation
For equal annual withdrawals that reduce the account to zero, use the annuity-withdrawal formula: annual withdrawal = $28,000 × r ÷ [1 − (1 + r)^−n]. For the 3-year plan, the total withdrawn is about $32,056.89; for the 4-year plan, it is about $32,174.36. The 4-year plan therefore yields the higher total, so the correct choice is “4 year account; $32,174.36.”
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