Say that you purchase a house for $254,000 by getting a mortgage for $225,000 an
ID: 2750103 • Letter: S
Question
Say that you purchase a house for $254,000 by getting a mortgage for $225,000 and paying a $29,000 down payment. If you get a 25-year mortgage with a 7 percent interest rate, what are the monthly payments? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
If the house appreciates at 3 percent per year, what will be the value of the house in ten years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
How much of this value is your equity? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
PMT $Explanation / Answer
Part A)
The monthly payment can be calculated with the use of PMT function of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,-PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value and FV = Future Value (if any)
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Using the information provided in the question, we get,
Rate = 7%/12, Nper = 25*12 = 300, PV = $225,000 and FV = 0
Using these values in the above function/formula for PMT, we get,
Monthly Payment = PMT(7%/12,300,-225000,0) = $1,590.25
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Part B)
To determine the amount of loan balance, we will have to calculate the future value of monthly payments (as calculated in Part A) and the present value of $225,000. The future value can be calculated with the use of FV function/formula of EXCEL/Financial Calculator. The function for FV is FV(Rate,Nper,PMT,PV) where Rate = Interest Rate, Nper = Period, PMT = Payment and PV = Present Value.
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Using the information provided in the question, we get,
Rate = 7%/12, Nper = 10*12 = 120, PMT = $1,590.25 and PV = $225,000
Future Value of Monthly Payments after 10 Years = FV(7%/12,120,1590.25,0) = $275,248.67
Future Value of $225,000 after 10 Years = FV(7%/12,120,0,225000) = $452,173.81
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Value of Loan Balance after 10 Years = 452,173.81 - 275,248.67 = $176,925.14
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Part C)
To calculate the value of house in 10 years, we need to the calculate the future value of $254,000 at the appreciation rate. The future value can be calculated with the use of FV function/formula of EXCEL/Financial Calculator. The function for FV is FV(Rate,Nper,PMT,PV) where Rate = Interest Rate, Nper = Period, PMT = Payment (If any) and PV = Present Value.
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Using the information provided in the question, we get,
Rate = 3%, Nper = 10, PMT = 0 and PV = $254,000
Future Value of House after 10 Years = FV(3%,10,0,254000) = $341,354.76
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Part D)
The value of equity is the difference between the Future Value of House after 10 Years (calculated in Part C) and Value of Loan Balance after 10 Years (calculated in Part B)
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Using the values calculated above, we get,
Equity = 341,354.76 - 176,925.14 = $164,429.62