Question

In: Finance

A home buyer buys a house for $ 1630000. She pays​ 20% cash, and takes a​...

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

Solutions

Expert Solution

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

jeff jeffy answered 2 years ago
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