Question

Ximena is trying to get a mortgage loan of $170,000. The bank quotes her a 15-year rate of 5.6% and a 30-year rate or 7.5%. Both of these loans involve equal monthly payment.

a. What is monthly payment for the 15-year loan? What is the total interest paid?

b. What is the monthly payment for the 30-year loan? What is the total interest paid?

c. What is the APR for each option?

Answer 1

a. What is monthly payment for the 15-year loan? What is the total interest paid?

EMI = [P x I x (1+I)^N]/[(1+I)^N-1]

P =loan amount or Principal = 170000

I = Interest rate per month = .056/12

N = the number of installments = 15*12 = 180

EMI = [170000*.056/12*(1+.056/12)^180]/[(1+.056/12)^180-1]

= [170000*.056/12*2.3118453918]/[2.3118453918-1]

= 1834.06401083/1.3118453918

= 1398.08

total interest paid = (emi*number of installments)-loan amount

= (1398.08* 180)-170000

= 251654.4-170000

= 81654.40

b. What is the monthly payment for the 30-year loan? What is the total interest paid?

EMI = [170000*.075/12*(1+.075/12)^360]/[(1+.075/12)^360-1]

= [170000*.075/12*9.42153390473]/[9.42153390473-1]

= 10010.3797738/8.42153390473

= 1188.66

total interest paid = (emi*number of installments)-loan amount

= (1398.08* 180)-170000

= 251654.4-170000

= 81654.40

c. What is the APR for each option?

APR is the annual rate charged on loan. IT is the rate as given in the loan agreement. SO the APR comes to 5.6% and 7.5% respectively.