It’s your 1st yr in college and you have agreed to loan a friend you met $3,000,
ID: 1167793 • Letter: I
Question
It’s your 1st yr in college and you have agreed to loan a friend you met $3,000, which your friend will pay you back for at then end of your 4 years. How much will your friend pay you at the end of the 4 years? How much interest will you receive from the loan? At:
a) Simple interest rate of 8% per year
b) Compound interest rate of 8% per year compounded annually
Now assume that you want to be paid back with an equal amount every year for four years.
c) How much would this annual payment be at a compound interest rate of 8% per year compounded annually?
d) At the end of the 4 years, how much will you friend have paid you? How much interest will you have received from the loan?
Explanation / Answer
(a) Amount after 4 years = $3,000 + $3,000 x 4 x 0.08 = $3,096
(b) Here, Amount after 4 years = $3,000 x (1.08)4 = $4,081.47
(c) $3,000 = Annual payment x Present value interest factor of annuity (8%, 4 years)
= Annual payment x 3.3121 (From PVIFA table)
Annual payment = $3,000 / 3.3121 = $905.77
(d) Total payment in 4 years = $905.77 x 4 = $3,623.08
Interest = $(3,623.08 - 3,000) = $623.08
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