You borrow $6000 to help pay your college expenses. You agree to repay the loan at the end of 5 years at 10% interest, compounded quarterly. (Round your answers to two decimal places.)
(a) What is the maturity value of the loan?
$ 


(b) How much interest are you paying on the loan?
$ 


To solve this, we'll use the compound interest formula:

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

where:
- $ A $ = the maturity value of the loan (future value)
- $ P $ = the principal amount (initial loan), which is $6000
- $ r $ = annual interest rate, which is 10% or 0.10
- $ n $ = number of times interest is compounded per year, which is quarterly or 4 times per year
- $ t $ = the time the money is borrowed, in years, which is 5 years

### Part (a): Calculate the Maturity Value of the Loan

Substituting these values into the formula:

\[
A = 6000 \left(1 + \frac{0.10}{4}\right)^{4 \cdot 5}
\]

#### Step-by-Step Calculation
1. Calculate the quarterly interest rate:  
   \[
   \frac{0.10}{4} = 0.025
   \]

2. Calculate the exponent for compounding:  
   \[
   4 \times 5 = 20
   \]

3. Substitute into the formula:
   \[
   A = 6000 \times (1 + 0.025)^{20}
   \]
   \[
   A = 6000 \times (1.025)^{20}
   \]

4. Now, calculate $ (1.025)^{20} \approx 1.63862 $.

5. Finally:
   \[
   A = 6000 \times 1.63862 \approx 9831.72
   \]

So, the maturity value of the loan is approximately **$9831.72**.

### Part (b): Calculate the Interest Paid on the Loan

The interest paid is the difference between the maturity value and the principal:

\[
\text{Interest} = A - P = 9831.72 - 6000 = 3831.72
\]

So, the interest paid on the loan is approximately **$3831.72**.

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Would you like further details on each step or have any questions?

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1. How does changing the compounding frequency affect the maturity value?
2. What would the maturity value be if interest was compounded monthly?
3. How would the maturity value differ if the interest rate was increased to 12%?
4. What is the impact of a shorter loan term on the interest paid?
5. How can this compound interest formula be applied to other real-life loan scenarios?

**Tip:** Compounding frequency has a significant effect on the maturity amount; more frequent compounding results in a higher maturity value.

You borrow $6000 to help pay your college expenses. You agree to repay the loan at the end of 5 years at 10% interest, compounded quarterly. (Round your answers to two decimal places.)
(a) What is the maturity value of the loan?
(b) How much interest are you paying on the loan?

Solve a real-life loan problem involving compound interest. Calculate the maturity value and interest paid on a $6000 loan with 10% annual interest compounded quarterly over 5 years. Learn the key steps using the compound interest formula. Suitable for Grades 11-12.

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