3. You have inherited funds from your grandmother’s estate and want to buy a property in
Florida which costs $250,000. You have enough funds for a 30% down payment and
you can obtain a mortgage for the balance at a five-year, fixed rate of 5.5% (APR
compounded semiannually). How much will you still owe at the end of five years
assuming a 20-year amortization period?
A) $147,172
B) $152,665
C) $195,625
D) $210,246
E) $224,825
Answer A
The mortgage amount is $250,000 x 70% = $175,000
The monthly interest rate is given by:
(1 + i
m )
12= 1 + EAR = (1 + 2.75%)² => (1 + i
m) = 1.0453168, that is i
m = 0.453168%
$175,000 = PMT x PVIFA(0.453168%,240)
PMT = $1,197.68
After 5 years, the outstanding mortgage (loan) will be the PV of the future remaining
mortgage payments (180 payments)
PV = $1,197.68 x PVIFA(0.453168%,180) = $147,171.66
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