You and your friend are comparing two loan options for a $165,000 house. Loan 1 is a 15-year loan with an annual interest rate of 3%. Loan 2 is a 30-year loan with an annual interest rate of 4%. Your friend claims the total amount repaid over the loan will be less for Loan 2. Is your friend correct? Justify your answer.

Answer:No, he is wrong.Step-by-step explanation:Since, the total payment of a loan after t years,[tex]A=P(1+r)^t[/tex]Where,P = present value of the loan,r = rate per period ,n = number of periods,Given,P = $165,000,In loan 1 :r = 3% = 0.03, t = 15 years,So, the total payment of the loan is,[tex]A_1 = 165000(1+0.03)^{15}=165000(1.03)^{15}\approx \$ 257,064.62[/tex]In loan 2 :r = 4% = 0.04, t = 30 years,So, the total payment of the loan is,[tex]A_2 = 165000(1+0.04)^{30}=165000(1.04)^{30}\approx \$ 535,160.59[/tex]Since, [tex]A_1 < A_2[/tex]Hence, total amount repaid over the loan will be less for Loan 1.That is, the friend is wrong.