Please show the equations used and show your work as if you were doing it by han
ID: 2614888 • Letter: P
Question
Please show the equations used and show your work as if you were doing it by hand.
Larry Davis borrows $80,000 at 14 percent interest toward the purchase of a home. His mortgage is for 25 years. a. How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.) b. How much interest will he pay over the life of the loan? c. How much should he be willing to pay to get out of a 14 percent mortgage and into a 10 percent mortgage with 25 years remaining on the mortgage? Assume current interest rates are 10 percent. Carefully consider the time value of money Disregard taxes.Explanation / Answer
Given:
Mortgage amount = $80,000
Interest rate=14 %
Term of mortgage=25 years (assume annual payments)
In c. Interest rate=10 percent
In a. annuity factor=6.873
In c. annuity factor=9.077
Solution:
a. A = PV /PV(14%, 25periods)= $80,000/6.873
Annual payment = $11,639.87
b. $11,639.75 annual payments × 25years = $290,993.75 - total payment $80,000.00
=total interest paidTotal interest over life of loan = $210,996.82
c. New payments at 10%
A = PV /PV(10%, 25periods)= $80,000/9.077= $8,813.48
Difference between old and new payments = $11,639.75old - 8,813.48new = $ 2,826.27difference
P.V. of difference = PVA = A x PVIFA (assume 10% discount rate, 25 periods)
= $ 2,826.27 x 9.077
Amount that could be paid to refinance = $25,654.05
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