Your bank offers to lend you $90,100 at an 8.5% annual interest rate to start your new business.The terms require you to amortize the loan with 10 equal end-of-year payments.How much interest would you be paying in Year 2?

Question

Quizplus · Accepted Answer

To calculate the interest payment in Year 2, we need to first calculate the payment amount using the annuity formula:
Payment = Loan amount / Present value factor of an annuity
Present value factor of an annuity for 10 periods at 8.5% annual interest rate = 6.7101
Payment = $90,100 / 6.7101 = $13,427.37 (rounded to nearest cent)
To calculate interest payment in Year 2, we need to use the formula:
Interest payment = Beginning balance × Interest rate
In Year 2, the beginning balance would be the remaining principal after the first payment is made. Using the formula for calculating the remaining principal after n payments:
Remaining principal after 1 payment = Payment × ((1 + r)^(n) - 1) / r
Where r is the interest rate per period and n is the number of payments.
r = 8.5% / 10 = 0.85%
n = 10 - 1 = 9 (number of payments remaining)
Remaining principal after 1 payment = $13,427.37 × ((1 + 0.0085)^(9) - 1) / 0.0085 = $94,402.78 (rounded to nearest cent)
Interest payment in Year 2 = $94,402.78 × 8.5% = $8,000.04 (rounded to nearest cent)
The closest answer choice is D) $7,142.26, which is not exact but the closest option.

Your Bank Offers to Lend You $90,100 at an 8