Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5.875%. Julio's monthly payments are $1,558.09. What percent of the purchase price was Julio's down payment? a. 13% b. 15% c. 18% d. 20%

Question

Adalyn Carney

Mathematics

27 November, 15:08

Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5.875%. Julio's monthly payments are $1,558.09. What percent of the purchase price was Julio's down payment? a. 13% b. 15% c. 18% d. 20%

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Nikhil Smith · Answer 1

P = { (rM) / [1 - (1 + r/n) ^ (-nt) ]}/n

where P = the payment, r = the annual rate, M = the mortgage amount, t = the number of years, and n = the number of payments per year.

Since we are given the payment, annual rate, number of years, and number of payement per year so we need to calculate first the mortgage amount M

1558.09 = { (0.05875*M) / [1 - (1 + 0.05875/12) ^ (-12*20) ]}/12

Solving for M

M = $ 219684.92

To solve the downpayment

D = 267900 - 21964.92 = $ 48125.08

Solving for the purchase price

T = 1558.09*12*20 = $373941.6

%D = ($ 48125.08/$373941.6) * 100 = 12.89 % about 13%