To calculate the quarterly payments for the loan, we can use the formula for the payment on an amortized loan:

$P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}$

Where:

• $P$ is the quarterly payment.
• $PV$ is the loan amount (the present value), which is $25,000.
• $r$ is the quarterly interest rate (annual interest rate divided by 4).
• $n$ is the total number of payments (number of quarters over 3 years).

Step 1: Calculate the Quarterly Interest Rate

The annual interest rate is 3%, so the quarterly interest rate is: $r = \frac{0.03}{4} = 0.0075$

Step 2: Calculate the Total Number of Payments

Since the loan is to be paid off in 3 years with quarterly payments, the total number of payments is: $n = 3 \times 4 = 12$

Step 3: Plug Values into the Formula

Now we can substitute the values into the payment formula:

$P = \frac{0.0075 \times 25,000}{1 - (1 + 0.0075)^{-12}}$

Step 4: Simplify the Expression

First, calculate $(1 + 0.0075)^{-12}$: $(1 + 0.0075)^{-12} = (1.0075)^{-12} \approx 0.91057$

Now, calculate the denominator: $1 - 0.91057 = 0.08943$

Finally, calculate the payment: $P = \frac{0.0075 \times 25,000}{0.08943} = \frac{187.5}{0.08943} \approx 2,096.83$

Result:

The quarterly payment is approximately $2,096.83.

Would you like further clarification on any step? Here are some related questions you might find helpful:

1. What would the payments be if the interest rate were 5% instead?
2. How much total interest will Shamut Construction pay over the 3 years?
3. What is the remaining balance after 1 year of payments?
4. How would the payment change if they took 5 years to pay off the loan instead of 3?
5. What if they made monthly payments instead of quarterly?

Tip: Understanding the effect of interest rate and loan period can help in making better financial decisions when borrowing.