You’ve decided to buy a house that is valued at $1 million. You have $250,000 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 $750,000 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. (Note: Round the final value of any interest rate used to four decimal places.)

$6581.58

Explanation:

Based on the information given in the question, the mortgage payment per month will be calculated thus:

= [P x I x (1+I)^N]/[(1+I)^N-1]

where,

P = Principal = $750000

I = Interest rate per month = 10%/12 = 0.10/12 = 0.008333

N = number of installments = 30 × 12 = 360

Then, the equated monthly installment will be:

= [750000 × 0.008333 × 1.008333^360] / [1.008333^360-1]

= [750000 × 0.008333 × 19.8350386989] / [19.8350386989 - 1]

= 123964/18.835

= 6581.58

Under this loan proposal, your mortgage payment will be $6581.58 per month.

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