Home Loan Problems Solution for Set 6 Question 1
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Solution to Question 1
For this type of question, you need this following equation:
A = i * P / (1 - (1 + i)^(-N) )
A is the payment Amount each month.
i is the interest rate as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Scott needs to borrow from the Pacific Western Bank is the principal P.
How many payment periods there are is represented by N.
Since Scott has a 5 % deposit, the principal P for the loan is actually the price of the apartment minus this deposit amount:
[an error occurred while processing this directive]P = 160000 - 0.01 * 5 * 160000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $152000
We need to convert the yearly interest rate into something we can use in this question - we need a monthly interest rate, so we need to divide by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 5.5 / 12 / 100
Monthly interest rate = 0.0046
We also need to calculate N, the total number of payments. Since payments occur every month, and Scott has a 15 year loan:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0046 * 152000 / (1 - (1 + 0.0046)^(-180) )
A = $1241.96
So every month, Scott will have to pay $1241.96 to the Pacific Western Bank.