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 calculate the cash price of the car Zinzi can buy, we need to consider both the deposit she has and the present value of the monthly payments she can make over 26 months.

### Step 1: Calculate the Present Value of the Annuity (Monthly Payments)
The formula for the present value of an annuity is:

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

where:
- \( P \) is the monthly payment = R2935
- \( r \) is the monthly interest rate = \(\frac{10.59\%}{12} = \frac{0.1059}{12} \approx 0.008825 \)
- \( n \) is the number of payments = 26

Plugging in the values:

\[
PV = 2935 \times \left(\frac{1 - (1 + 0.008825)^{-26}}{0.008825}\right)
\]

### Step 2: Add the Deposit to the Present Value
After calculating the present value, we add the deposit of R10735 to find the cash price of the car.

Let's calculate it step by step.The cash price of the car that Zinzi can buy is **R78,656.96**.

Do you want more details or have any questions?

Here are 5 related questions that might interest you:
1. How would the cash price change if the interest rate increased to 12%?
2. What if Zinzi could afford to make payments for 36 months instead of 26?
3. How much total interest will Zinzi pay over the 26 months?
4. What would be the impact if Zinzi decided to make a larger deposit?
5. How would the cash price change if the monthly payments were increased to R3500?

**Tip:** When dealing with loans or annuities, always remember that the longer the payment period, the more interest will accumulate, affecting the total cost.

Learn how to calculate the cash price of a car based on monthly payments and a deposit. This problem involves finance concepts such as annuities and compound interest. Zinzi can afford monthly payments of R2935 with a deposit of R10735 at an interest rate of 10.59% per year, compounded monthly, over 26 months. Discover the detailed solution and explore related scenarios.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation