12. You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. What will your annual payment be if you sign this mortgage? ( $24,176)

The Annual Payment will be $24,176.

Explanation:

First we need to calculate the loan amount as follow

Loan = Cost of House - Down payment = $350,000 - $50,000 = $300,000

Now use following formula to calculate the annual payment

PV of Annuity = Annuity Payment x ( 1 - ( 1 + interest rate )^-Numbers of periods ) / Interest rates

Where

PV of Annuity = Loan = $300,000

Interest rate = 7%

Numbers of periods = 30 years

Annuity Payment =  Annual payment = ?

Pacing values in the formula

$300,000 = Annual Payment x ( 1 - ( 1 + 7% )^-30 ) / 7%

$300,000 = Annual Payment x 12.409

Anual Payment = $300,000 / 12.409

Anual Payment = $24,176.00