Ntombi wants to open a Paint-and-Decor Shop and borrows R450 000 from Uncle Sakhile. She realises that she will only be able to start paying him back five years from now. Money is worth 9,8% per year, compounded every three months.

The amount of money that Ntombi will owe Uncle Sakhile five years from now is

To determine the amount of money Ntombi will owe Uncle Sakhile five years from now, we need to calculate the future value of the loan using the compound interest formula.

The compound interest formula is:

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

Where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (initial amount of money).
- \( r \) is the annual nominal interest rate (as a decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested or borrowed for, in years.

Given:
- \( P = \text{R}450,000 \)
- \( r = 9.8\% = 0.098 \)
- \( n = 4 \) (since the interest is compounded every three months)
- \( t = 5 \) years

Now, let's plug these values into the formula:

\[
A = 450,000 \left(1 + \frac{0.098}{4}\right)^{4 \times 5}
\]

Let's calculate this step by step.The amount of money that Ntombi will owe Uncle Sakhile five years from now is approximately **R730,216.71**.

Would you like any further details on this calculation or have any other questions? 

Here are some related questions you might be interested in:
1. How would the amount change if the interest was compounded monthly instead of quarterly?
2. What if Ntombi could start paying back after 3 years? How would that affect the amount owed?
3. How is compound interest different from simple interest in terms of growth over time?
4. What would the interest rate need to be for Ntombi to owe exactly R700,000 after five years?
5. How would the amount owed change if the loan was R500,000 instead of R450,000?

**Tip:** Understanding how interest compounds over time can help in making better financial decisions when taking out loans or investing money.

Ntombi wants to open a Paint-and-Decor Shop and borrows R450 000 from Uncle Sakhile. She realizes that she will only be able to start paying him back five years from now. Money is worth 9.8% per year, compounded every three months. The amount of money that Ntombi will owe Uncle Sakhile five years from now is

Discover how to calculate the future value of Ntombi's R450,000 loan using the compound interest formula. This problem involves key mathematical concepts like compound interest and exponential growth, and is suitable for students in Grades 10-12.

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