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.