Question

Go to the St. Louis Federal Reserve FRED database, and find data on the interest rate on a four-year auto loan (TERMCBAUTO48NS). Assume that you borrow \(20,000 to purchase a new automobile and that you finance it with a four-year loan at the most recent interest rate given in the database. If you make one payment per year for four years, what will the yearly payment be? What is the total amount that will be paid out on the \)20,000 loan?

Short answer

Yearly payment - $5,878.03.

Total payment - $23,512.12

Step-by-step solution

Step 1. Introduction

The interest rate is an amount charged by the lender on borrowings. It also refers to the amount paid to depositors on deposits. In the given case, the interest rate refers to the amount charged on borrowing an auto loan.

Step 2. Explanation

$\$5,878.03\times 4=\$23,512.12$The interest rate on four-year auto loan for is 4.58% for November 2021.

The yearly payment can be obtained as,

$$\begin{gathered} \$20,000=FP\times \left[\frac{1}{1+0.0458}+\frac{1}{{(1+0.0458)}^2}+\frac{1}{{(1+0.0458)}^3}+\frac{1}{{(1+0.0458)}^4}\right] \\ \$20,000=FP\times \left[0.9562+0.9144+0.6959+0.8360\right] \\ \$20,000=FP\times 3.4025 \\ FP=\frac{20,000}{3.4025}=5,878.03 \end{gathered}$$

The total payment for the perio of four years can be obtained as,

$\$5,878.03\times 4=\$23,512.12$