Question

Carlos pays $25 for skis and borrows the remaining amount. The loan payments are $75 every 3 months for 1/1/2 years. The interest rate is 16.2%/a compounded quarterly. What was the selling price of the skis?

Answer 1

$417.52

Explanation:

Present value of annuity = P * {1-[1/(1+r)^n]/r}

P =Periodic payment i.e. 75

r = rate of interest per period i.e. 16.2% /4 = 4.05% or 0.0405

n =no. of compounding period i.e. 1.50*4 =6

Present value of annuity = Loan amount

Present value of annuity = 75 * {1-[1/(1+0.0405)^6]/0.0405}

Present value of annuity = 75 * {1-[1/(1.0405)^6]/0.0405}

Present value of annuity = 75 * {1-[1/1.268973)/0.0405}

Present value of annuity = 75 * (1-0.78804)/0.0405

Present value of annuity = 75 * (0.21196/0.0405)

Present value of annuity = 75 * 5.23361

Present value of annuity = 392.52

Loan amount = $392.52

Selling price = $392.52 + $25.00

Selling price = $417.52

Thus, the selling price of the skis is $417.52