Ross purchased a new commercial vehicle today for $25,000. The entire amount was financed using a five-year loan with a 4 percent interest rate (compounded monthly). How much will Ross owe on his vehicle loan after making payments for three years (i.e., when two years of payments remain)?

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To find out how much Ross will owe on his vehicle loan after making payments for three years, we can use the formula for the remaining balance on an installment loan, which is a form of the present value of an annuity formula. The loan details are as follows: the principal amount (P) = $25,000, the annual interest rate (r) = 4% or 0.04 (when expressed as a decimal), the number of payments per year (n) = 12 (monthly payments), and the total number of payments (t) = 5 years * 12 months/year = 60 payments. The number of payments remaining after 3 years = 2 years * 12 months/year = 24 payments.The monthly interest rate = annual interest rate / number of payments per year = 0.04 / 12 = 0.003333.The monthly payment (M) can be calculated using the formula for the payment on an installment loan:$$M = P \times \frac{r/n}{1 - (1 + r/n)^{-nt}}$$$$M = 25000 \times \frac{0.003333}{1 - (1 + 0.003333)^{-60}}$$$$M ≈ 460.27$$The remaining balance (B) after 3 years (or after making 36 payments) can be calculated using the formula for the present value of an annuity (since it represents the present value of the remaining payments):$$B = M \times \frac{1 - (1 + r/n)^{-n(t - 3)}}{r/n}$$$$B = 460.27 \times \frac{1 - (1 + 0.003333)^{-24}}{0.003333}$$$$B ≈ 10602.44$$Therefore, after making payments for three years, Ross will owe approximately $10,602.44 on his vehicle loan.

Ross Purchased a New Commercial Vehicle Today for $25,000