I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.
A. Find the value of the mortgage on their house? (1 mark)
B. Find the value of the monthly payment? (3 marks)
C. Find the loan outstanding after making 20 payments? (4 marks)
D. Find the principal repaid in the 21st payment? (5 marks)
Answers
Given : A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at 9% p.a. to be amortized over 30 years with monthly payments.
To find : value of the mortgage on their house , value of the monthly payment
Solution:
House worth = $326,000
Paid amount = $ 75000
Remaining amount = 326,000 - 75000 = $251,000
value of the mortgage on their house = $251,000
EMI Formula = [P x (R/100) x (1+(R/100)ⁿ]/[(1+(R/100)ⁿ-1]
P = 251000
R = 9 % per annum = 9/12 % per month = 0.75 % per month
n = 30 years = 360 months
EMI = Equated Monthly Payments
EMI = 251000 (0.75/100) * (1.0075)³⁶⁰ / ( (1.0075)³⁶⁰ -1)
=> EMI = 2019.6
loan outstanding after 20 payments = $ 248053.5
Principle repaid in 21st payment = $159.2
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