You want to buy a new sports car from Muscle Motors for $32,500. The contract is in the form of a 36-month annuity due at an APR of 6.55 percent. What will your monthly payment be?

Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

To find the monthly payment for the annuity due, we can use the annuity due formula for the present value of an annuity:

\[
PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r)
\]

Where:
- $ PV $ is the present value of the loan (the price of the car),
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate,
- $ n $ is the number of payments (36 months in this case).

We are solving for $ P $, the monthly payment.

### Given:
- $ PV = 32,500 $
- APR = 6.55% (annual percentage rate)
- $ n = 36 $ months (3 years)
- Monthly interest rate, $ r = \frac{6.55\%}{12} = \frac{0.0655}{12} \approx 0.0054583 $

Rearranging the formula to solve for $ P $:

\[
P = \frac{PV}{\left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r)}
\]

Let's calculate it.The monthly payment for the car will be approximately **$991.42**.

Would you like further details on the calculation or have any questions?

Here are five related questions for further exploration:
1. How would the monthly payment change if the APR was lower, such as 5%?
2. What would the payment be for a 48-month loan at the same APR?
3. How much interest will be paid over the course of the loan?
4. What is the total amount paid by the end of the loan?
5. How does an annuity due differ from an ordinary annuity in terms of payment timing?

**Tip:** In an annuity due, payments are made at the beginning of each period, which slightly increases the payment amount compared to an ordinary annuity.

You want to buy a new sports car from Muscle Motors for $32,500. The contract is in the form of a 36-month annuity due at an APR of 6.55 percent. What will your monthly payment be? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

Learn how to calculate the monthly payment for a $32,500 sports car using a 36-month annuity due contract with a 6.55% APR. Follow this step-by-step solution to apply the annuity due formula and find the payment amount with intermediate calculations rounded to 2 decimal places.

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