SOLUTION: The buyer of a house will pay $7500 cash and $1000 at the end of each 3 months for 12 years. If money is worth 9% compounded quarterly, find (a) the cash value of the house; (b)

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Question 1194506: The buyer of a house will pay $7500 cash and $1000 at the end of each 3 months for 12 years. If money
is worth 9% compounded quarterly, find
(a) the cash value of the house;
(b) the remaining liability of the debtor just after he pays his 10th installment of $1000;
(c) his remaining liability just before he pays the 10th installment.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the down payment is equal to 7500.
the payments are 1000 at the end of each quarter (3 months is a quarter) for 12 * 4 = 48 quarters at 9%/4 = 2.25% per quarter.
the present value of that is equal to 29,169.55.
add the down payment of 7500 to get a cash value of the house equal to 36,669.55.
after the 10th payment, the remaining balance on the loan is equal to 25,362.99.
before the 10th payment, the remaining balance on the loan is equal to 26,362.99.
you can use the calculator at https://arachnoid.com/finance/ to get these results.
first analysis is for 48 quarters shown below:

second analysis is for 38 quarters shown below:

after the 10th payment, there are 38 quarters left to pay.
the present value of the second analysis is the remaining balance after the 10th payment.
add 1000 to that to get the remaining balance before the 10th payment.
i also solved the problem using excel to get the end of quarter display of the remaining balance.
that is shown below.

let me know if you have any questions.
theo