Say that you purchase a house for $290,000 by getting a mortgage for $255,000 an
ID: 2717154 • Letter: S
Question
Say that you purchase a house for $290,000 by getting a mortgage for $255,000 and paying a $35,000 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.)
PMT $__________
PVA $ ___________
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.
Equity $___________
What would the loan balance be in ten years? (Round the payment amount to the nearest cent but do not round any other interim calculations. Round your final answer to 2 decimal places.)Explanation / Answer
Answer
Monthly Mortgage Loan instalment = $ 1,802.76
Loan Balance after 10 years = $200,515.16
Value of the house after 10 years = $ 389,735.75
Equity in House = $ 189,220.59
Cost of House = $ 290,000
Down Payment = $ 35,000
Loan Amount L = $ 255,000
Rate of interest r = 7% per annum or 7%/12 = 0.583333% per month
Mortgage Period n = 25 years or 25*12 = 300 months
Let PMT denote monthly loan payment which can be calculated as below
PMT = L * [(r*(1+r)^n)/((1+r)^n – 1)]
PMT = 255000 * [(0.00583333 * (1+0.00583333)^300)/((1+0.00583333)^300 – 1)]
= 255000 * [(0.00583333 * (1.00583333)^300)/((1.00583333)^300 – 1)]
= 255000 * [(0.00583333 * 5.7254182093)/((5.7254182093 – 1)]
= 255000 * (0.03339827288/4.724182093)
= 255000 * 0.007069641
= 1802.75853 or 1802.76 (rounded off)
Loan balance outstanding in 10 years or after 10*12 = 120 months can be calculated as below
Loan Balance B = L[((1+r)^n – (1+r)^p)/((1+r)^n -1)]
B = 255000 * [((1+0.00583333)^300 – (1+0.00583333)^120)/((1+0.00583333)^300 – 1)]
= 255000 * {((1.00583333)^300 – (1.00583333)^120)/ ((1+0.00583333)^300 – 1)]
= 255000 * [(5.7254182093 – 2.0096613767)/(5.7254182093-1)]
= 255000 * (3.7157568326/4.7254182093)
= 255000 * 0.78633396411
B = 200,515.160848 or 200,515.16 (rounded off)
Purchase price of house = $ 290,000
Annual appreciation rate = 3%
Value of the house after 10 years = 290000 * (1+0.03)^10
= 290000*1.03^10
= 290000 * 1.343916379
= 389,735.75000975 or 389,735.75 (rounded off)
Equity in House = Value of house after 10 years - Loan Balance after 10 years
= $ 389,735.75 - $ 200,515.16
= $ 189,220.59