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.

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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 1 year ago

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