To calculate the maturity value and the interest charged on a loan, we will use the compound interest formula:

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

Where:

• $A$ is the maturity value (the total amount owed, including interest).
• $P$ is the principal (initial loan amount), which is $7,500.
• $r$ is the annual interest rate (4.8% or 0.048).
• $n$ is the number of compounding periods per year. Since it is compounded monthly, $n = 12$.
• $t$ is the time in years. Since the loan is for 16 months, $t = \frac{16}{12} = \frac{4}{3}$ years.

Step 1: Plug in the values into the formula

$A = 7,500 \left(1 + \frac{0.048}{12}\right)^{12 \times \frac{4}{3}}$

Simplifying the terms inside the parentheses:

$A = 7,500 \left(1 + 0.004\right)^{16}$ $A = 7,500 \left(1.004\right)^{16}$ Now, calculate $1.004^{16}$:

$1.004^{16} \approx 1.06743$

So,

$A \approx 7,500 \times 1.06743 = 8,005.725$

Step 2: Find the interest charged by subtracting the principal from the maturity value:

$\text{Interest} = A - P = 8,005.725 - 7,500 = 505.725$

Final Answer:

• The maturity value of the loan is approximately $8,005.73.
• The interest charged is approximately $505.73.

Would you like a more detailed explanation or further assistance?

Related Questions:

1. How would the maturity value change if the interest rate were different?
2. What would happen if the loan was compounded quarterly instead of monthly?
3. How does the number of compounding periods affect the total interest charged?
4. How do you calculate the maturity value for simple interest instead of compound interest?
5. How would the maturity value change if the loan duration were shorter or longer?

Tip: Compound interest grows faster as the number of compounding periods increases. The more frequently interest is compounded, the higher the maturity value.