The Turners have purchased a house for $140,000. They made an initial down payme

Question

The Turners have purchased a house for $140,000. They made an initial down payment of $20,000 and secured a mortgage with interest charged at the rate of 9%/year compounded monthly on the unpaid balance. The loan is to be amortized over 30 yr. (Round your answers to the nearest cent.) (a) What monthly payment will the Turners be required to make? $ 965.55 (b) How much total interest will they pay on the loan? $ 227596.97 (c) What will be their equity after 10 years? $107315.69X (d) What will be their equity after 22 years? $65906.74X

Explanation / Answer

Answer 1 We can use the present value of annuity formula to calculate the monthly loan payment. PV of annuity = P*{[1-(1+r)^-n]/r} PV of annuity = Loan amount = $140000 - $20000 = $120000 P = Periodic payment i.e. Monthly loan payment = ? rate of interest per month = 9%/12 = 0.0075 n = no.of months = 30 years * 12 = 360 120000 = P*{[1-(1+0.0075)^-360]/0.0075} 120000 = P*124.28 P = 965.55 Monthly loan payment = $965.55 Answer 2 Calculation of total interest payment on loan Total Payment = 360 * $965.55 = $347,596.97 Less : Loan amount $120,000.00 Total Interest Payment $227,596.97 Answer 3 Calculation of Loan balance after 10 years and Equity We can use the present value of annuity formula to calculate the loan balance after 10 years. PV of annuity = P*{[1-(1+r)^-n]/r} PV of annuity = Loan balance = ? P = Monthly loan payment = $965.55 rate of interest per month = 9%/12 = 0.0075 n = no.of months remaining = 20 years * 12 = 240 PV of annuity = 965.55*{[1-(1+0.0075)^-240]/0.0075} PV of annuity = 965.55 * 111.14 Loan balance after 10 years = $1,07,318.01 Equity after 10 years = Cost of home - Loan balance after 10 years = $140000 - $107318.01 = $32,683.99 Answer 4 Calculation of Loan balance after 22 years and Equity We can use the present value of annuity formula to calculate the loan balance after 10 years. PV of annuity = P*{[1-(1+r)^-n]/r} PV of annuity = Loan balance = ? P = Monthly loan payment = $965.55 rate of interest per month = 9%/12 = 0.0075 n = no.of months remaining = 8 years * 12 = 96 PV of annuity = 965.55*{[1-(1+0.0075)^-96]/0.0075} PV of annuity = 965.55 * 68.26 Loan balance after 22 years = $65,906.94 Equity after 22 years = Cost of home - Loan balance after 10 years = $140000 - $65906.94 = $74,093.06

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