Question

Vanessa bought a house for $268,500. She has a 30 year mortgage with a fixed rate of 6.25%. Vanessaâs monthly payments are $1,595.85. How much was Vanessaâs down payment?
a. $9,314.45
b. $16,781.25
c. $40,275.00
d. $53,040.00
Please select the best answer from the choices provided A B C D

Answer 1

Answer:

Ans. A) $9,314.45

Explanation:

Hi, first we have to bring to present value the monthly payments to be made for 30 years (360 months). In order for this to be useful, we have to convert this annua compounded monthly rate (6.25%) to an effective rate, that is 6.25% / 12 = 0.5208%. Now, when we find this present value, we are going to substract it from the price of the house and that is the value of the down payment. But let´s just go ahead and do it together.

We have to use this formula to bring to present value the $1,595.85 monthly payments, for 30 years (360 months) at a rate of 6.25% (0.5208% monthly).

$PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

It should look like this

$PresentValue=\frac{1,595.85((1+ 0.005208 )^{360}-1) }{0.005208(1+0.005208)^{360} }$

$Present Value=259,185.55$

Now, let´s go ahead and find the down payment.

$DownPayment=Price-PresentValue$

$DownPayment=268,500-259,185.55= 9,314.45$

So, the answer is a). $9,314.45

Best of luck.