Question

11. [12pt] A homeowner obtains a loan called a mortgage from a bank for 130,000 dollars. The loan has a yearly interest rate of 6.9 percent, which is compounded monthly. That is, each month the amount that the homeowner still owes increases by 6.9/12 0.575 percent of the amount currently owed (called interest). The loan is intended to last for 102 months. So, after making 102 total payments (all equal in amount), the homeowner will have paid back not only the total amount of the loan, but also all the interest owed. What are: 1) the amount of each monthly payment in dollars required by the homeowner, and 2) the percentage of the loan that was payed as interest? Do not enter any units. Answer 1 of 2: Answer 2 of 2: Submit All Answers

Answer 1

Loan amount = 130,000$ Yearly interest rate = 6.9% monthly compounded Total payment in 102 months A = P(1 + r/n)^(nt) P = 130000 r = 0.069 n = 12 nt = 102 A = 130000(1 + 0.069/12)^102 = 233306.8870$ Total amount pard 1) at each month = 233306.8870/102 = 2287.322$ (equal for all month) 2) % loan that pard as interest = 233306.8870 - 130000/130000 times 100 = 103306.8870/130000 times 100 = 79.46%