Home Loan Problems Solution for Set 7 Question 1
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Solution to Question 1
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 expressed as a decimal (NOT A PERCENTAGE!), for the period of time over which payments are made.
P is the principal - this is the amount that Uriel needs to borrow from the TrustCo Bank.
N is the number of payment periods.
Because the deposit it 28 %, Uriel's principal amount will be the cost of the house less this deposit amount:
P = 530000 - 0.01 * 28 * 530000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $381600
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 11.8 / 12 / 100
Monthly interest rate = 0.0098
We also need to calculate N, the total number of payments. Since payments occur every month, and Uriel has a 10 year loan:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0098 * 381600 / (1 - (1 + 0.0098)^(-120) )
A = $5430.82
So every month, Uriel will have to pay $5430.82 to the TrustCo Bank.