You borrow $8000 to help pay your college expenses. You agree to repay the loan at the end of 7 years at 10% interest, compounded quarterly.What is the maturity value of the loan?

To calculate the maturity value (future value) of the loan, we can use the compound interest formula:

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

Where:
- $A$ is the maturity value (future value) of the loan,
- $P$ is the principal amount (\$8000),
- $r$ is the annual interest rate (10% or 0.10),
- $n$ is the number of times interest is compounded per year (quarterly means $n = 4$),
- $t$ is the time the money is invested or borrowed for (7 years).

Now, let's plug in the values:

\[
A = 8000 \left( 1 + \frac{0.10}{4} \right)^{4 \times 7}
\]
\[
A = 8000 \left( 1 + 0.025 \right)^{28}
\]
\[
A = 8000 \left( 1.025 \right)^{28}
\]

I'll calculate the result now.The maturity value of the loan after 7 years, compounded quarterly at 10% interest, is approximately **$15,971.96**.

Would you like more details on how this was calculated, or do you have any further questions?

Here are 5 related questions to further explore:
1. How would the maturity value change if the interest were compounded monthly instead of quarterly?
2. What if the interest rate was reduced to 8%? How would that affect the future value?
3. How much interest would you end up paying in total?
4. How would the maturity value change if the loan term was only 5 years instead of 7?
5. What is the difference between simple interest and compound interest for this loan?

**Tip**: The more frequently interest is compounded, the higher the future value, as interest builds on itself more often!

You borrow $8000 to help pay your college expenses. You agree to repay the loan at the end of 7 years at 10% interest, compounded quarterly. What is the maturity value of the loan?

Learn how to calculate the maturity value of an $8000 loan with 10% interest compounded quarterly over 7 years. This step-by-step solution applies the compound interest formula and helps students understand exponential growth in financial mathematics. Suitable for high school students.

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