The Taylors have purchased a $150,000 house. They made an initial down payment o
ID: 2646697 • Letter: T
Question
The Taylors have purchased a $150,000 house. They made an initial down payment of $30,000 and secured a mortgage with interest charged at the rate of 7%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Round your answer to the nearest cent.)
What is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years? (Round your answers to the nearest cent.)
Explanation / Answer
SOLUTION:
Using loan calculator we find the monthly payment as $997.95
The value (balance due) of the mortgage after n payments = the future value of the original loan - the future value ordinary annuity FVOA of the payments. To solve for equity after n payments (assuming no appreciation) subtract the loan amount from the purchase price of $150,000.
Since there are monthly payments, r = 0.07 / 12 = 0.00583
Calculation of equity after 5 years,
FV Principal = P (1 + r)n
FV Principal = $150,000 (1.00583)5yrs * 12months/year = $212,601.51
FVOA of the payments will be,
FVOA = PMT[(( 1 + r )n) -1) / r]
FVOA = $997.95 [(1.0058360)
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