You borrow $16,000 at 8 percent interest to buy a car and repay
it in four equal payments at the end of each of the next 4 years.
What are the annual payments?

To calculate the annual payments for a loan using equal payments over a fixed period, we can use the formula for the **annuity payment**:

\[
A = \frac{P \cdot r}{1 - (1 + r)^{-n}}
\]

Where:
- $ A $ = annual payment
- $ P $ = principal (loan amount) = \$16,000
- $ r $ = interest rate per period = 8% = 0.08
- $ n $ = number of periods = 4 years

Now, substituting the values:

\[
A = \frac{16,000 \cdot 0.08}{1 - (1 + 0.08)^{-4}}
\]

Let me calculate this for you.The annual payments required to repay the $16,000 loan over 4 years at 8% interest are approximately **$4,830.73**.

Do you want more details or have any questions?

Here are 5 related questions to consider:
1. How would the payments change if the interest rate were lower or higher?
2. What would happen if the loan term were extended to 5 years?
3. Can you calculate the total interest paid over the loan period?
4. How is this formula related to mortgage payments?
5. What would happen if payments were made monthly instead of annually?

**Tip:** It's always useful to know your total interest cost. For that, you can multiply the annual payment by the number of years and subtract the principal.

You borrow $16,000 at 8 percent interest to buy a car and repay it in four equal payments at the end of each of the next 4 years. What are the annual payments?

Find out how to calculate the annual payments required to repay a $16,000 loan over 4 years with 8% interest using the annuity payment formula. Learn about key finance concepts like loan amortization and time value of money. This is ideal for students in grades 11-12 or college-level finance courses.

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