question archive Joyce lends a sum of money to her friend and expects to receive a lump sum cash return of $100,000 at the end of five years
Joyce lends a sum of money to her friend and expects to receive a lump sum cash return of $100,000 at the end of five years
Subject:FinancePrice:2.86 Bought10
Joyce lends a sum of money to her friend and expects to receive a lump sum cash return of $100,000 at the end of five years. If she believes that a 9 percent annual return compounded quarterly is a reasonable return to earn on this loan. How much should she lend to her friend? 1. A) $17,843.09 2. B) $52,147.18 3. C) $64,081.65 4. D) $89,471.23
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Answer:
PV = FV / (1 + r / m)mn
PV = Present value
FV = Future value = $100000
r = rate of interest = 9%
m = number of compounding periods based on frequency = 4
n = Number of years = 5 years
PV = FV / (1 + r / m)mn
= $100000 / (1 + 0.09 / 4)4*5
= $100000 / (1 + 0.0225)20
= $100000 / (1.0225)20
= $100000 / 1.56050920059
= $64081.6471714 rounded off to $64081.65
She should lend to her friend $64081.65
Therefore, the correct answer is C) $64081.65
