Zinzi is buying a car today. She can afford to make monthly payments of R2935 at the end of every month and has enough saved for a deposit of R10735. If she must pay interest at a rate of 10.59% per year, compounded monthly, and she wants to make exactly 26 payments, what is the cash-price of the car that she can buy? (Give your answer rounded to 2 decimal places. If you think the answer is R1012.3456, type in 1012.35)

To determine the cash price of the car that Zinzi can buy, we need to calculate the present value of the annuity (the loan amount) and then add the deposit she has saved.

The formula for the present value of an annuity is:

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

Where:
- \( P \) is the monthly payment amount: \( R2935 \)
- \( r \) is the monthly interest rate: \( \frac{10.59\%}{12} \)
- \( n \) is the number of payments: \( 26 \)

Given:
- Monthly interest rate \( r = \frac{10.59\%}{12} = \frac{0.1059}{12} \approx 0.008825 \)

After calculating the present value \( PV \), we'll add the deposit \( R10735 \) to get the total cash price of the car.

Let's compute this.The cash price of the car that Zinzi can buy is **R78,656.96**.

Would you like more details on this calculation, or do you have any questions? Here are some related questions you might find useful:

1. What would be the cash price if the interest rate were lower?
2. How much total interest will Zinzi pay over the 26 payments?
3. How would the cash price change if Zinzi made more payments?
4. What if Zinzi wanted to make a balloon payment at the end?
5. How does the deposit amount affect the total loan amount?

**Tip:** When considering car loans, it's important to compare different interest rates and loan terms to find the most cost-effective option.

Learn how to calculate the cash price of a car that Zinzi can afford, given monthly payments, a deposit, and a compound interest rate. Detailed step-by-step solution provided with calculations and explanations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation