
Thendo has to pay Rendi R27 000 twenty-five months from now. He decides to pay her back earlier. If a simple interest rate of 9,4% per year is applicable, then the amount that Rendi will receive from Thendo 12 months from now is

To calculate the amount that Rendi will receive from Thendo if he pays her back 12 months from now, we need to use the formula for the present value (PV) in the context of simple interest:

\[
PV = \frac{FV}{1 + rt}
\]

Where:
- \( PV \) is the present value (the amount Rendi will receive 12 months from now).
- \( FV \) is the future value (R27 000).
- \( r \) is the annual interest rate (9.4% or 0.094).
- \( t \) is the time in years between the early payment and the original due date.

**Step 1: Determine the time period \( t \)**

The original payment is due 25 months from now, but Thendo wants to pay 12 months from now. So, the time period \( t \) is the difference between 25 months and 12 months:

\[
t = \frac{25 - 12}{12} = \frac{13}{12} \text{ years}
\]

**Step 2: Substitute the values into the formula**

\[
PV = \frac{27 000}{1 + (0.094 \times \frac{13}{12})}
\]

**Step 3: Calculate the present value**

First, calculate the interest:

\[
1 + (0.094 \times \frac{13}{12}) = 1 + 0.1017 = 1.1017
\]

Now, calculate the present value:

\[
PV = \frac{27 000}{1.1017} \approx 24 505.08
\]

So, the amount that Rendi will receive from Thendo 12 months from now is approximately **R24 505.08**.

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Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would the amount change if the interest rate were 10% instead of 9.4%?
2. What would be the impact if Thendo decided to pay 6 months earlier instead of 13?
3. How is simple interest different from compound interest in loan repayment?
4. How can you calculate the interest earned over the 13-month period?
5. What if Thendo had chosen to pay Rendi in full 24 months from now?
6. How do different time periods affect the present value of a payment?
7. What is the formula for future value in the context of simple interest?
8. How would inflation affect the real value of R24 505.08 over time?

**Tip:** When calculating present value, it's essential to accurately determine the time period to ensure correct interest calculations.

Learn how to calculate the amount Rendi will receive from Thendo if he pays her back 12 months early using a simple interest rate of 9.4% per year. The present value formula is used to determine the amount based on the future value and time period involved.

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