Home Loan Problems Solution for Set 3 Question 4
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Solution to Question 4
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 Kaleb needs to borrow from the Columbia State Bank.
N is the number of payment periods.
Since Kaleb has a 27 % deposit, the principal P for the loan is actually the price of the three bedroom apartment minus this deposit amount:
[an error occurred while processing this directive]P = 270000 - 0.01 * 27 * 270000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $197100
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 = 3.4 / 12 / 100
Monthly interest rate = 0.0028
We also need to calculate N, the total number of payments. Since payments occur every month, and Kaleb has a 20 year loan:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0028 * 197100 / (1 - (1 + 0.0028)^(-240) )
A = $1132.99
Finally the solution: every month, Kaleb is going to have to fork out $1132.99 to the Columbia State Bank to pay off his loan.