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Jackson is buying a house for $244,000. He puts 20% down then finances the balance for...

Jackson is buying a house for $244,000. He puts 20% down then finances the balance for 30 years at 4.75% interest. The monthly homeowners association dues are $135 per month. Home insurance totals $1842 per year, and annual taxes are $3120. Assuming home owner association fees, taxes and insurance are added monthly to the total house payment, find the total monthly amount that Jackson will pay for the house.

Expert Solution

Value of the house = $244000

Downpayment = 20% of 244000 = $48800

=> Loan Amount P = $244000 - $48800 = $195200

Interest Rate = 4.75% or 0.0475/12 monthly

Number of payment periods = n = 30*12 = 360 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, Monthly Payments = rP(1+r)^N/[(1+r)^N-1]

= 195200*( 0.0475/12)*(1+ 0.0475/12)³⁶⁰/((1+ 0.0475/12)³⁶⁰-1) = $1018.26

Monthly association dues = $135

Monthly insurance = 1842/12 = $153.5

Monthly Taxes = 3120/12 = $260

Hence total monthly payments = $1018.26 + 135 +153.5 + 260 = $1566.76

jeff jeffy answered 2 years ago

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