Loans accruing compound interest. What percentage is the total interest accrued of the original loan if $430 is borrowed at 1% pa compound interest for 7 years.

To calculate the total interest accrued on a loan using compound interest, we can use the compound interest formula:

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

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

Since the interest is compounded annually, $ n = 1 $. Now, let’s calculate the total amount after 7 years for a loan of \$430 at an interest rate of 1% per year:

\[
A = 430 \left(1 + \frac{0.01}{1}\right)^{1 \times 7}
\]
\[
A = 430 \times (1.01)^7
\]

Let's compute that.The total amount after 7 years is approximately \$461.02.

Now, to find the total interest accrued, we subtract the original loan from the final amount:

\[
\text{Interest} = A - P = 461.02 - 430 = 31.02
\]

Next, the percentage of the total interest accrued relative to the original loan is:

\[
\text{Percentage} = \frac{\text{Interest}}{P} \times 100 = \frac{31.02}{430} \times 100
\]

Let’s compute that.The total interest accrued over 7 years is approximately 7.21% of the original loan amount.

Would you like further details or have any questions?

Here are five related questions to explore:
1. How does the frequency of compounding affect the total interest?
2. What would the interest be if the rate were 2% instead of 1%?
3. How much interest would accrue over a different time period, such as 10 years?
4. How would monthly compounding affect the total interest?
5. What would be the result if \$500 were borrowed instead of \$430?

**Tip:** Compound interest grows faster when compounded more frequently, even if the rate stays the same!

Learn how to calculate the percentage of total interest accrued on a $430 loan at 1% per annum compound interest over 7 years. This solution uses the compound interest formula and is suitable for high school students in Grades 10-12.

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