A man buys a house for $200,000. He makes a $50,000 down payment and agrees to amortize the rest of the debt with quarterly payments over the next 10 years. If the interest on the debt is 12%, compounded quarterly, find
(i) Size of the quarterly payments, (4 marks)
(ii) Total amount of the payments, and (4 marks)
(iii) Total amount of interest paid. (4 marks)
Answers
Answer:
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Given:- Cost of house= 200000
down payment = 50000
no of years= 10
To find:- (i) Size of the quarterly payments, (4 marks)
(ii) Total amount of the payments, and (4 marks)
(iii) Total amount of interest paid. (4 marks)
Solution:-
We know that from given information
An= 200000-50000
= 150000
it is the remaining amount to be loaned after down payment.
Now, n= 4(10) = 40
i = 12/100*4 = 0.12/4 = 0.03
Thus for the quarterly payment we have,
R = 150000*(0.3/(1-0.3^-40))
R = 150000*0.04326
R = 6489.36 dollars
the man made 40 payments of 6489.36 so his payment totalled,
=40*6489.36
=259574.40 dollars
plus the 50000 down payment so it becomes 309574.40
Out of the 309574.40 paid 20000 was paid for payment of house. The remaining 109574.40 was total amount of interest paid.
The required answers are 6489.36 ,309574.40, 109574.40 repectively.