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Homework answers / question archive / The cost of a home you want to purchase is $260,000
The cost of a home you want to purchase is $260,000.00. To qualify for a mortgage, your lender wants a 20% down payment. Your mortgage interest rate is 4% for 30 years and you have to pay 4 points.
A. How much money do you need for the down payment?
B. How much will your mortgage be?
C. How much will you have to pay for the points?
D. What is the monthly payment?
E. By the end of the loan what will be the total of all your payments?
F. What is the total interest you will have paid on your mortgage by the end of the loan?
Solution to A
Down payment required is 20% of Purchase price of Home.
So Down payment = $ 260,000 x 0.2 = $ 52,000
Solution to B
Mortgage amount will be difference of cost of home and down payment
Mortgage amount = $ 260,000 - $ 52,000 = $ 208,000
Solution to C
Points are the upfront charges paid to the lender as part of mortgage arrangement. 4 points on a mortgage means 4% of the mortgage amount.
So amount to be paid for points = $ 208,000 x 0.04 = $ 8,320
Solution to D
Now monthly payment for mortgage is calculated by below formula-
Monthly payment = Mortgage amount x r x (1 + r)n
(1 + r)n - 1
Where r is the monthly interest rate = 4% /12 = 0.33% = 0.0033
n is the number of months = 30 years x 12 = 360 months
Monthly payment = 208000 x 0.0033 x (1 + 0.0033)360
(1 + 0.0033)360 - 1
= 686.4 x 3.2741
3.2741 – 1
= 2247.3422
2.2741
Monthly payment = $ 988.23
Solution to E
Total payments by end of loan = Monthly payments x number of months
= 988.23 x 360
Total payments by end of loan = $ 355,762.8
Solution to F
Interest paid = Total payments by end of loan – Mortgage amount
= $ 355,762.8 - $ 208,000
Interest paid = $ 147,762.8
