Question

Samantha received a loan of $14,000 at 5.25% compounded quarterly. She had to make payments at the end of every quarter for a period of 1 year to settle the loan. Calculate the size of payments. 3,568.75 Round to the nearest cent

Answer 1

To calculate the size of payments for Samantha's loan, we can use the formula for the present value of a loan. Plugging in the given values, the size of payments comes out to be approximately $500.20.

Step-by-step explanation:

To calculate the size of payments, we can use the formula for the present value of a loan:

Present Value = Payment × [(1 - (1 + Interest Rate) ^ -n)] / Interest Rate

Where:

• Present Value is the loan amount received
• Payment is the size of payments
• Interest Rate is the annual interest rate divided by the number of compounding periods per year
• n is the total number of compounding periods

In this case, the loan amount is $14,000, the interest rate is 5.25% compounded quarterly (or 1.3125% per quarter), and the total number of compounding periods is 4 (1 year with quarterly payments). Plugging these values into the formula:

Present Value = Payment × [(1 - (1 + 0.013125) ^ -4)] / 0.013125

Simplifying the equation:

Payment × [1 - (1 + 0.013125) ^ -4] = $14,000 × 0.013125

Now, we can solve for the size of payments:

Payment × 0.366812 = $183.75

Payment = $183.75 / 0.366812 = $500.20 (rounded to the nearest cent)