3
QuizMultiple Choice

Amortization — Quiz

Question 3 • Financial Algebra/Mathematics

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 return over the duration of the loan, given that the account will be zeroed out by the end of that period?

Answer
A
4 year account; 42 dollars comma 742 point 5 2
B
4 year account; 32 dollars comma 174 point 3 6
C
3 year account; 32 dollars comma 056 point 8 9
D
3 year account; 24 dollars comma 130 point 7 7

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 annual withdrawals of about $8,043.59, or $32,174.36 in total. The 3-year plan at 7.083% gives about $10,685.63 per year, or $32,056.89 total. The 4-year account therefore yields the higher total return: $32,174.36.

AI-written and checked against the verified answer.

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