Final answer:
To calculate the quarterly loan payments for Fox's $500,000 loan at 12% annual interest over ten years, we use the annuity payment formula, factoring in the principal amount, quarterly interest rate, and total number of payments.
Step-by-step explanation:
Fox is seeking a loan of $500,000 to expand his business, to be repaid over ten years with a 12% annual interest rate, in equal quarterly installments. Calculating the quarterly installments for a loan requires understanding of loan amortization, which is the process of spreading out a loan into a series of fixed payments over time. In Fox's case, the loan will be repaid in 40 installments (10 years x 4 quarters per year).
The formula for calculating the payment for an annuity based on future value which is applicable here is:
PMT = PV * i / (1 - (1 + i)^-n)
where PMT is the quarterly payment, PV is the present value of the loan ($500,000), i is the quarterly interest rate (12% annual rate divided by 4, hence 3% per quarter), and n is the total number of payments (40).
Using the formula, the quarterly payment can be calculated as:
PMT = 500,000 * 0.03 / (1 - (1 + 0.03)^-40)
After performing the calculations, we would obtain the amount that represents the quarterly installment Fox will need to pay to service the debt over the tenure of the loan.