Question

You’ve decided to buy a house that is valued at $1 million. You have $350,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $650,000 mortgage, and is offering a standard 30-year mortgage at a 10% fixed nominal interest rate (called the loan’s annual percentage rate or APR). Under this loan proposal, your mortgage payment will be ____ per month

(A) $7,130.03
(B) $8,841.23
(C) $5,704.02
(D) $7,700.43

Answer 1

Answer:

Correct option is (C)

Explanation:

Given:

Mortgage amount (PV) = $650,000

APR = 10%

Per month interest rate (rate) = 10% ÷ 12 = 0.8333% or 0.008333

Mortgage period (nper) = 30 years or 30×12 = 360 months

Monthly payment can be calculated using spreadsheet function =pmt(rate,nper,PV)

Monthly payment is computed as $5,704.02

PMT is negative as it is a cash outflow.

Answer 2

Answer:

P = $5704.02  i.e. correct option is C

Explanation:

given data:

Period of mortgage 30 year = ( 30* 12 = 360 month)

Loan of $650,000 for 30 year is approved by bank

Annual interest rate is 10% so, monthly rate is (10%/12 = 0.833)

monthly mortgage is calculated as

$PV = P [\frac{1-(1+r)^{-n}}{r}]$

substitute value to obtain montly payment

$650,000 = P [\frac{1-(1+\frac{.1}{12})^{-360}}{\frac{.1}{12}}]$

$\frac{650000}{[\frac{1-(1+\frac{.1}{12})^{-360}}{\frac{.1}{12}}]} = P$

P = $5704.02