Question

You plan to purchase a $180,000 house using a 15-year mortgage obtained from your local credit union. The mortgage rate offered to you is 5.5 percent. You will make a down payment of 10 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 20th payment.
c. Calculate the amount of interest and, separately, principal paid in the 110th payment.
d. Calculate the amount of interest paid over the life of this mortgage.

(For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

cost of house		180000
Down payment-10% of cost of house	180000*10%	18000
amount borrowed		162000
Monthly Interest rate	5.5/12	0.46%
period = n = 15*12		180
1-
Monthly payment = amount borrowed/PVAF at .45833% for 180 months	162000/122.38692	1323.67
PVAF at .45833% for 180 months	1-(1+r)^-n / r r =.45833% n =180	.560936/.45833%	122.3869265
2-
Balance at the end of year 19th monthly payment	PV*(1+r)^n -[ Monthly payment* (1+r)^n-1 / r)]	162000*(1.0045833)^19 - [1323.67* (1.0045833^19 -1 )/.45833%	176704.7-[1323.67*(.09077/.45833%)	176704.7-26214.59	150490.11
Balance at the end of 19th payment		150490.11
Monthly payment = amount borrowed/PVAF at .45833% for 180 months		1323.67
Interest = balance at the end of 19th payment *monthly interest rate	150490.11*.45833%	689.7413212
Principal payment in 20th payment = Monthly payment-Interest	1323.67-689.74	633.93
3-
Balance at the end of year 109th monthly payment	PV*(1+r)^n -[ Monthly payment* (1+r)^n-1 / r)]	162000*(1.0045833)^109 - [1323.67* (1.0045833^109 -1 )/.45833%	266676.1-[1323.67*(.646149/.45833%)	266676.1-186609.5	80066.6
Balance at the end of 109th payment		80066.6
Monthly payment = amount borrowed/PVAF at .45833% for 180 months		1323.67
Interest = balance at the end of 109th payment *monthly interest rate	80066.6*.45833%	366.9692478
Principal payment in 110th payment = Monthly payment-Interest	1323.67-366.9692	956.7007522
4-
total Interest paid over the loan period =(monthly payment*no. of payment)-Principal borrowed	(1323.67*180)-162000	76260.6