John Harper has borrowed $17,400 to pay for his new truck. The annual interest rate on the loan is 9.4 percent, and the loan needs to be repaid in four payments. What will be his annual payment if he begins his payment beginning now

$4,953

Explanation:

Given by the question, we have:

+) Present value of annuity  = $17,400

+) Return on the investment = annual interest rate on the loan = 9.4%

The type of this annuity is annuity due.

We have the equation to calculate the present value of annuity due as following:

PV Annuity Due = P × [1 - (1 + r)^(-N)]/r × (1+r)

=> P = PV Annuity Due ÷ {[1 - (1 + r)^(-N)]/r × (1+r)}

In which:

+) P: Annual payment

+) r: annual interest rate = 9.4% = 0.094

+) N: Number of payments = 4 (As the loan is repaid in 4 payments)

+) PV Annuity Due = 17,400

=> P = 17,400 ÷ {[1 - (1 + 0.094)^(-4)]/0.094 × (1+0.094)} ≈ $4,953

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