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

a.

R24 877,68.

b.

R22 578,40.

c.

R24 700,77.

d.

R24 504,61.

To determine the amount Thendo has to pay Rendi 12 months from now, we need to calculate the present value of the R27,000 that is due 25 months from now using the simple interest formula.

The formula for calculating the present value \( P \) is:

\[ P = \frac{A}{1 + r \times t} \]

Where:
- \( A \) is the future value (R27,000)
- \( r \) is the annual interest rate (9.4% or 0.094 as a decimal)
- \( t \) is the time period in years

In this case, the time period \( t \) is the difference between the 25 months and the 12 months, which is 13 months or \(\frac{13}{12}\) years.

Substitute the values into the formula:

\[ P = \frac{27000}{1 + 0.094 \times \frac{13}{12}} \]

First, calculate the denominator:

\[ 1 + 0.094 \times \frac{13}{12} = 1 + 0.094 \times 1.0833333 \approx 1 + 0.1018333 \approx 1.1018333 \]

Now, divide the future value by this result:

\[ P = \frac{27000}{1.1018333} \approx 24487.68 \]

Therefore, the correct answer is:

a. R24 877,68

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How is the present value different from the future value in financial calculations?
2. What is the formula for simple interest?
3. How would the calculation change if the interest rate was compounded monthly?
4. Can you explain the concept of discounting in financial terms?
5. What would be the effect of a lower interest rate on the present value?
6. How do you convert months into years for interest calculations?
7. How does simple interest differ from compound interest over different periods?
8. What are some practical applications of present value calculations?

**Tip:** When dealing with financial calculations involving time, ensure to consistently convert all time periods to the same unit (e.g., years) to maintain accuracy.

Learn how to calculate the future value using the simple interest formula with an example problem. Understand the concepts of simple interest, present value, and interest rate calculation. Suitable for high school students and those interested in financial mathematics.

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