Question

1. You purchase a $350,000 town home and you pay 25% down. You obtain a 30 year fixed rate mortgage with an annual interest rate of 6.25%. After 5 years you refinance the mortgage for 25 years at a 5% annual interest rate. After you refinance what is the new monthly payment?

2. You plan to purchase a $175,000 house using a 15-year mortgage obtained from your local bank. The mortgage rate offered to you is 7.75%. You will make a down payment of 20 percent of the purchase price.

(a) Calculate your monthly payments on this mortgage.

(b) Calculate the amount of interest and, separately, principal paid in the 60^thpayment.

(c) Calculate the amount of interest and, separately, principal paid in the 180^th(last) payment.   

(d) Calculate the amount of interest paid over the life of this mortgage.

Answer 1

1. Present Value of town home = $350,000

Down Payment = $350,000 * 0.25 = $87,500

Loan Amount = $262,500

rate per period = 0.0625 / 12 = 0.0052

No of installments = 30*12 = 360

Current PMT = (Loan amount * rate per period) / [ 1 - (1 + rate per period) ^ - no of installments]

= ($262,500 * 0.0052) / [ 1 - (1+0.0052) ^-360]

= $1,614.55

Outstanding amount after 5 years = loan amount * (1 +rate per period) ^ no of installments paid - PMT * [{(1 + rate per period ) ^ no of installment paid - 1} / rate per period]

= $262,500 * (1 + 0.0052) ^ 60 - $1,614.55 *[{(1 + 0.0052) ^60 -1}/0.0052]

=$358,325.82 - $113,344.75

=$244,918.07

New rate per period = 0.05/12 = 0.0042

No of installments = 25*12 = 300

New PMT =(Loan amount * rate per period) / [ 1 - (1 + rate per period) ^ - no of installments]

=($244,918.07 * 0.0042) / [ 1 - (1 + 0.0042) ^-300]

=$1,437.48

2. Current value of house = $175,000

Down payment = $175,000 * 0.20 = $35,000

Loan Amount = $175,000 - $35,000 = $140,000

Rate per installment = 0.0775/12 = 0.006458

No of installment = 15*12 = 180

a. PMT = (Loan amount * rate per period) / [ 1 - (1 + rate per period) ^ - no of installments]

= ($140,000 * 0.006458) / [ 1 - (1 + 0.006458) ^ - 180]

= $1,317.75

b. Outstanding amount after 59 installments = loan amount * (1 +rate per period) ^ no of installments paid - PMT * [{(1 + rate per period ) ^ no of installment paid - 1} / rate per period]

= $140,000 * (1 + 0.006458 ) ^ 59 - $1,317.75 * [ { ( 1 +0.0.006458) ^ 59 - 1} / 0.006458]

= $204,678.28 - $94,268.24

=$110,410.04

Interest payment for 60th installment = $110,410.04 * 0.006458 = $713.03

Principal paid for 60th installment = PMT - $713.03 = $1,317.75 - $713.03 = $604.72

c. Outstanding amount after 179 installments = loan amount * (1 +rate per period) ^ no of installments paid - PMT * [{(1 + rate per period ) ^ no of installment paid - 1} / rate per period]

= $140,000 * (1+0.006458) ^ 179 - $1317.75 * [{(1+0.006458) ^ 179 - 1} / 0.006458]

=$443,149.75 - $441,832.00

=$1317.75

Interest payment for 180th payment = $1,317.75 * 0.006458 = $8.51

Principal paid for 180th payment = $1,317.75 - $8.51 = $1,309.24

d. Total amount of interest paid over life of mortgage = loan amount * { rate per period * no of installments / [ 1 - (1 + rate per month) ^(-no of installments)] -1}

= $140,000 * { 0.006458 * 180 / [1 - (1+0.006458) ^ (-180)] - 1}

= $97,195.72