Home Loan Problems Solution for Set 2 Question 7
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Solution to Question 7
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 Houston needs to borrow from the Pacific National Bank is the principal P.
N is the number of payment periods.
Because the deposit it 8 %, Houston's principal amount will be the cost of the one bedroom house less this deposit amount:
[an error occurred while processing this directive]P = 520000 - 0.01 * 8 * 520000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $478400
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 = 9.3 / 12 / 100
Monthly interest rate = 0.0077
We also need to calculate N, the total number of payments. The repayments happen every month. Houston's loan runs for 25 years, so we can calculate how many months he'll be making payments for:
N = 12 * 25
N = 300
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0077 * 478400 / (1 - (1 + 0.0077)^(-300) )
A = $4113.44
So every month, Houston will have to pay $4113.44 to the Pacific National Bank.