Question

You plan to purchase a $150,000 house using a 15-year mortgage obtained from your local credit union. The mortgage rate offered to you is 6.25 percent. You will make a down payment of 10 percent of the purchase price.

a.	Calculate your monthly payments on this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Monthly payment

$

b.	Calculate the amount of interest and, separately, principal paid in the 20th payment. (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Amount of interest	$
Amount of principal	$

c.	Calculate the amount of interest and, separately, principal paid in the 150th payment. (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Amount of interest	$
Amount of principal	$

d.	Calculate the amount of interest paid over the life of this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Amount of interest paid

$

Answer 1

Answer a

Loan borrowed from local credit union = $150000 * 90% = $1,35,000

Using present value of annuity formula , we can calculate the monthly mortgage payment.

Present value of annuity = P *{[1 - (1+r)^-n]/r}

Present value of annuity = Original loan amount = $135000

P = monthly payment = ?

r = rate of interest per month = 6.25%/12 = 0.005208

n = no.of months payments = 15 years * 12 = 180

135000 = P *{[1 - (1+0.005208)^-180]/0.005208}

135000 = P *{0.60744 / 0.005208}

135000 = P * 116.63

P = 1157.52

Monthly Payment = $1157.52

Answer b

Calculation of interest and principal paid in the 20th payment.

First step is to find out the loan outstanding amount at the end of 19th installment using present value of annuity formula.

Present value of annuity = P *{[1 - (1+r)^-n]/r}

P = monthly payment = $1157.52

r = rate of interest per month = 6.25%/12 = 0.005208

n = no.of months payments remaining = 161

Present value of annuity = 1157.52 *{[1 - (1+0.005208)^-161]/0.005208}

Present value of annuity = 1157.52 * 108.8098

Present value of annuity = 125949.89

Loan outstanding amount at the end of 19th installment = $1,25,949.89

Amount of interest in 20th payment = Loan outstanding amount at the end of 19th installment * Monthly interest rate = $125949.89 * 0.005208 = $655.99

Amount of principal paid in 20th payment = $1157.52 - $655.99 = $501.53

Answer c

Calculation of interest and principal paid in the 150th payment.

First step is to find out the loan outstanding amount at the end of 149th installment using present value of annuity formula.

Present value of annuity = P *{[1 - (1+r)^-n]/r}

P = monthly payment = $1157.52

r = rate of interest per month = 6.25%/12 = 0.005208

n = no.of months payments remaining = 31

Present value of annuity = 1157.52 *{[1 - (1+0.005208)^-31]/0.005208}

Present value of annuity = 1157.52 * 28.55832

Present value of annuity = 33056.89

Loan outstanding amount at the end of 149th installment = $33,056.89

Amount of interest in 150th payment = Loan outstanding amount at the end of 149th installment * Monthly interest rate = $33056.89 * 0.005208 = $172.17

Amount of principal paid in 150th payment = $1157.52 - $172.17 = $985.35

Answer d

Calculation of the amount of interest paid over the life of this mortgage.

Total Loan payments = Monthly payment * no.of monthly payments =

$208,353.60

Less : Original Loan amount

$135,000.00

Amount of Interest paid over the life of the mortgage

$73,353.60