
Dembe received an amount of R2 340 from the bank at a discount rate of 12% per annum at the beginning of September. The future value of the loan at the beginning of July the following year is

To calculate the future value of the loan that Dembe received, we can use the formula for the future value with simple interest:

\[
FV = \frac{P}{(1 - rt)}
\]

Where:
- \( FV \) is the future value (what we need to find).
- \( P \) is the present value (R2 340 in this case).
- \( r \) is the annual discount rate (12% or 0.12).
- \( t \) is the time period in years.

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

Dembe received the loan at the beginning of September, and we need to calculate the future value at the beginning of July the following year. The time from the beginning of September to the beginning of July is 10 months.

To convert months into years:
\[
t = \frac{10}{12} = \frac{5}{6} \text{ years}
\]

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

\[
FV = \frac{2340}{(1 - 0.12 \times \frac{5}{6})}
\]

**Step 3: Calculate the future value**

\[
FV = \frac{2340}{1 - 0.1} = \frac{2340}{0.9}
\]

\[
FV = 2600
\]

So, the future value of the loan at the beginning of July the following year is **R2 600**.

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Would you like further details or have any questions?

Here are some related questions for further exploration:

1. What is the difference between simple interest and compound interest?
2. How does the time period affect the future value in a discount loan?
3. How can the discount rate be converted into an equivalent interest rate?
4. What is the formula for the future value of an amount in compound interest?
5. How do different types of loans affect repayment schedules?
6. What would be the future value if the discount rate were 10% instead of 12%?
7. How would the calculation change if the loan was taken for 1 year exactly?
8. How does inflation impact the real value of the future amount received?

**Tip:** When dealing with financial calculations, always double-check the time period and the rate type (annual, semi-annual, etc.) to ensure accuracy.

Learn how to calculate the future value of a loan received at a 12% discount rate using simple interest. Follow a step-by-step solution to find out the future amount of R2 340 received in September, projected to R2 600 by the following July. Suitable for students and professionals interested in financial mathematics.

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