1. My friend Roger has a home mortgage for $88,500 with an interest rate of 5.12
ID: 2722453 • Letter: 1
Question
1. My friend Roger has a home mortgage for $88,500 with an interest rate of 5.125% annual compounded monthly and a period of 15 years. He made his first monthly payment in May of 2003. Now he wants to take out a home improvement loan for $20,000 with an interest rate of 4.5% annual compounded monthly and a period of 5 years. He will make his first monthly payment in June of 2016.
a) What is the monthly payment for his home mortgage?
b) What is the monthly payment for his home improvement loan?
c) From June 2016 to the end of the mortgage, how much interest will be paid on the mortgage?
d) From June 2016 to the end of the home improvement loan, how much interest will be paid on the home improvement loan?
Roger has an option of rolling in the remaining balance of his home mortgage into the home improvement loan and payoff his mortgage in June of 2016. His regular June mortgage payment will be rolled into the home improvement loan.
a) If he does this, what is the new loan value of the home improvement loan?
b) What is the new payment of the home improvement loan?
c) What is the total interest paid on the home improvement loan?
Explanation / Answer
I
a) . EMI (MONTHLY PAYMENT) = LOAN AMT / PVAF
PVAF,0.05125,15 YEARS = 125.42
SO EMI = 88500/125.42 = $ 705.629 PER MONTH
b). EMI (MONTHLY PAYMENT) = LOAN AMT / PVAF
PVAF,0.00375, 5 YEARS = 53.693
SO EMI = 2000/53.693 = $ 37.2488 PER MONTH
c). INTEREST = (EMI * NO. OF MONTHS) - LOAN
= ( 125.42 * 180 ) - 88500 = $ 38513.22
d) INTEREST = (EMI * NO. OF MONTHS) - LOAN
= ( 37.2488 * 60 ) - 20000 = $ 234.928
II.
a) Amount outstanding on June 2016 (13 Year after actual grant of loan) would be $8625.39. (Derived by adjusting PVAF for 13 Years and PVAF for remaing 2 Years) . So total loan would be 8625.39+20000 = $ 28625.39 loan for 5 years at 4.5% Interest.
b) EMI = 28625.39/53.693 = $ 533.13
c) Interest = (533.13 * 60 ) - 28625.39 = $ 3362.41
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