Muriel would like to borrow $55,000 to pay one year’s tuition at a private U.S. university. She would like to make quarterly payments and finish repaying the loan in 4 years. If the bank is quoting her a rate of 8 percent compounded monthly. Determine her quarterly payment.
To determine Muriel's quarterly payment, we can use the formula for the quarterly payment of a loan. The formula is:
Quarterly Payment = (Loan Amount * Quarterly Interest Rate) / (1 - (1 + Quarterly Interest Rate)^(-Number of Payments))
First, let's calculate the Quarterly Interest Rate. The annual interest rate of 8 percent compounded monthly needs to be converted to a quarterly rate. Since there are 12 months in a year and 4 quarters in a year, the Quarterly Interest Rate can be calculated as:
Quarterly Interest Rate = (1 + Annual Interest Rate / 12)^3 - 1 = (1 + 0.08 / 12)^3 - 1
Next, let's calculate the Number of Payments. Muriel wants to finish repaying the loan in 4 years. Since she wants to make quarterly payments, the Number of Payments is calculated as:
Number of Payments = 4 years * 4 quarters/year = 16 quarters
Now we have all the required values to calculate the Quarterly Payment. We can substitute the values into the formula:
Quarterly Payment = ($55,000 * Quarterly Interest Rate) / (1 - (1 + Quarterly Interest Rate)^(-Number of Payments))
Plugging in the values, we can solve for the Quarterly Payment.