Enele invests an amount of money in an account earning 13,88% interest per year, compounded weekly. After five years, this amount has accumulated to R50 000. The amount that was invested initially is

a.

R25 001,79.

b.

R15 300,00.

c.

R34 700,00.

d.

R29 515,94.

To find the initial amount that Enele invested, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A = 50\,000 \) (the accumulated amount after 5 years)
- \( r = 13.88\% = 0.1388 \) (annual interest rate)
- \( n = 52 \times 7 = 364 \) (compounded weekly)
- \( t = 5 \) years
- \( P \) is the initial amount (the unknown we want to find)

We can rearrange the formula to solve for \( P \):

\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]

Let's substitute the given values into the equation and calculate \( P \).The initial amount that Enele invested is approximately **R24,981.99**.

This value is very close to option **a. R25,001.79**.

Would you like more details or have any other questions?

Here are 8 related questions to further explore this topic:
1. How does the initial investment change if the interest rate increases?
2. What would the initial amount be if the interest were compounded monthly instead of weekly?
3. How much interest did Enele earn over the 5 years?
4. How does the compounding frequency impact the final amount in the account?
5. What would happen if the interest rate was 10% instead of 13.88%?
6. Can you show how to derive the formula for compound interest from the basic principles?
7. How much would Enele's investment be worth after 10 years instead of 5?
8. What is the effective annual rate (EAR) for this investment?

**Tip:** Understanding the impact of compounding frequency on interest earned can help in making more informed investment decisions.

Learn how to calculate the initial investment using compound interest in Enele's investment problem. Understand the impact of interest rates and compounding frequency on investment growth. Suitable for advanced high school students.

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