Home Loan Problems Solution for Set 3 Question 5
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Solution to Question 5
The equation you need to use is as follows:
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.
P is the principal - this is the amount that Randall needs to borrow from the Center Bank.
How many payment periods there are is represented by N.
Since Randall has a 17 % deposit, the principal P for the loan is actually the price of the house minus this deposit amount:
[an error occurred while processing this directive]P = 230000 - 0.01 * 17 * 230000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $190900
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. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 2.9 / 12 / 100
Monthly interest rate = 0.0024
We also need to calculate N, the total number of payments. Since payments occur every month, and Randall 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 = 0.0024 * 190900 / (1 - (1 + 0.0024)^(-180) )
A = $1309.18
So every month, Randall will have to pay $1309.18 to the Center Bank.