Question

Humphrey purchases a 100,000 home. Mortgage payments are to be made monthly for 30 years, with the first payment to be made one month from now. The annual effective rate of interest is 5 percent. After 10 years, the amount of each monthly payment is increased by 325.40 in order to repay the mortgage more quickly. Calculate the amount of interest paid over the duration of the loan. ADAPT note: The monthly payments after 10 years are still firm, not an increasing annuity. 66,300 68,500 70,100 70,700 74,400

Answer 1

OPTION A

rate compounded monthly r=(((1+5%)^(1/12)-1)*12)

Monthly payment=PMT(r/12,12*30,-100000)

Loan outstanding after 10 years=FV(r/12,12*10,PMT(r/12,12*30,-100000),-100000)

Number of payments required=NPER(r/12,-325.40-PMT(r/12,12*30,-100000),-100000),FV(r/12,12*10,PMT(r/12,12*30,-100000),-100000))

Amount of interest paid=NPER((((1+5%)^(1/12)-1)*12)/12,-(PMT((((1+5%)^(1/12)-1)*12)/12,12*30,-100000)+325.40),FV((((1+5%)^(1/12)-1)*12)/12,12*10,PMT((((1+5%)^(1/12)-1)*12)/12,12*30,-100000),-100000))*(PMT((((1+5%)^(1/12)-1)*12)/12,12*30,-100000)+325.40)+10*12*PMT((((1+5%)^(1/12)-1)*12)/12,12*30,-100000)-100000

=66262.471081