math help!! Finance

Question

You want to buy a $244,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan for the rest.

a) How much is the loan amount going to be?

b) what will your monthly payments be if the interest rate is 6%?

c) what will your monthly payments be if the interest rate is 7%?

Answer 1

The 20% down payment = .5*244,000 = 48,800. Hence you must finance is 244,000-48,800 = 195,200.. which is the Present Value of the payments.

The Present value is PV= Payment*K where K= ((1/i)(1-(1/(1+i))^T

Here, T = 30*12 = 360 months. When i= 6% annual the monthlu rate is 6%/12 = .5%

k₀₆ = (1/.0005)(1- (1/(1.005))^T) = 200( 1- (.166))) = 166.79

pmt = 195200/166.79 = 1170.32

k₀₇= (1/(7%/12))(1- (1/(1+.06/12))³⁶⁰)) = 150.31 pmt = 195200*150.31 = 1298.67

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