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Bill O’Brien would like to take his wife, Mary, on a trip three years from now to Europe to celebrate their 40th anniversary
Bill O’Brien would like to take his wife, Mary, on a trip three years from now to Europe to celebrate their 40th anniversary. He has just received a $24,000 inheritance from an uncle and intends to invest it for the trip. Bill estimates the trip will cost $32,160. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
What interest rate, compounded annually, must Bill earn to accumulate enough to pay for the trip? (Round your interest rate to the nearest whole percentage.)
Expert Solution
Answer)
Calculation of annual interest rate
Future Value = Present value X Future value factor at required rate for 3 years
$ 32,160 = $ 24,000 X Future value factor at required rate for 3 years
Future value factor at required rate for 3 years = $ 32,160/ $ 24,000
Future value factor at required rate for 3 years = 1.34
On a perusal of future value of $ 1 table the value in 3 years row corresponding to 10% is 1.3310 and 11% is 1.3676. It implies that the annual rate of interest lies in between these two rates and can be calculated by interpolating between these two rates.
Annual interest rate = 10 + (1.3676 – 1.34)/ (1.3676 – 1.3310)
= 10 + (0.0276/ 0.0366)
= 10 + 0.75
= 10.75%
Therefore the annual rate of interest is 10.75% approximately.
Final Answer: The question requires that final answer to be rounded to nearest whole percentage.
Therefore, the annual rate of interest is 11% (rounded off).
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