bank offers to lend you $100,000 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

The loan is amortized which means that each payment consists of both principal and interest. 
The annual payment can be calculated using the formula:

PMT = (r * PV) / (1 - (1+r)^-n)

where
PV = present value of the loan = $100,000
r = interest rate per period = 8.5% / 1 = 0.085
n = total number of periods = 10

PMT = (0.085 * 100,000) / (1 - (1+0.085)^-10) = $16,470.17

To find the interest paid in Year 2, we need to calculate the interest portion of the second payment.

First, we can find the principal paid in the first year by subtracting the interest from the first payment from the total loan amount.

Interest in Year 1: 
interest1 = r * PV = 0.085 * 100,000 = $8,500

Principal in Year 1: 
principal1 = PMT - interest1 = $16,470.17 - $8,500 = $7,970.17

Next, we can use the principal in Year 1 to calculate the remaining loan balance at the end of Year 1.

Loan balance at end of Year 1: 
balance1 = PV - principal1 = $100,000 - $7,970.17 = $92,029.83

Finally, we can calculate the interest portion of the second payment based on the remaining loan balance at the end of Year 1.

Interest in Year 2: 
interest2 = r * balance1 = 0.085 * 92,029.83 = $7,826.84

Therefore, the answer is B) $7,927.

Bank Offers to Lend You $100,000 at an 8