To determine the size of each quarterly installment for the loan, we can use the loan amortization formula, which is similar to the formula for calculating the payment on an annuity.

Given:

• Principal (loan amount) $P = 6,000$
• Annual interest rate $r = 13\% = 0.13$
• Compounding frequency = quarterly (4 times per year)
• Time $t = 2$ years
• Number of quarters $n = 2 \times 4 = 8$ (since payments are made quarterly)

Step 1: Calculate the quarterly interest rate

Since the loan is compounded quarterly, the quarterly interest rate $i$ is given by: $i = \frac{r}{4} = \frac{0.13}{4} = 0.0325$

Step 2: Use the amortization formula

The formula for the installment payment $A$ is: $A = \frac{P \cdot i}{1 - (1 + i)^{-n}}$ where:

• $A$ is the size of each installment
• $P$ is the loan amount
• $i$ is the quarterly interest rate
• $n$ is the total number of quarters

Step 3: Plug in the values

$A = \frac{6000 \times 0.0325}{1 - (1 + 0.0325)^{-8}}$

Now, let’s calculate this.

The size of each quarterly installment is approximately $863.78.

Would you like a more detailed breakdown of the calculations, or do you have any further questions?

Here are five related questions you might find interesting:

1. How does the loan repayment schedule affect the total interest paid?
2. How would the size of the installments change with a higher or lower interest rate?
3. What would happen to the payment amount if the loan term were extended to 3 years?
4. How can early repayments reduce the total interest paid?
5. What is the impact of compounding frequency on the loan repayment?

Tip: When repaying a loan, making extra payments towards the principal can significantly reduce the overall interest cost.