In: Finance
A home buyer buys a house for $ 1630000. She pays 20% cash, and takes a fixed-rate mortgage for ten years at 8.75% APR. If she makes semi-monthly payments, which of the following is closest to each of her payment?
A. $ 9794.42
B. $ 6529.62
C. $ 8162.02
D. $ 8978.22
Purchase price = $1,630,000
Cash paid = 20% of purchase price
= $1,630,000 * 20%
= $326,000
Therefore,
Mortgage = Purchase price - cash paid
= $1,630,000 - $326,000
= $1,304,000
We can use the present value of annuity formula, to find the answer:
Where,
PVA = Present Value of Annuity
A = Annuity or Payment
i = rate of interest in decimal form
n = number of years
a = number of payments per year
na = total number of payments
When payments are semi-monthly, there will be 2 payments in a month and 24 payments in a year. Therefore, a = 24
Now substituting the values in the formula, we get:
Therefore, the answer is C. $8162.02