Home Loan Problems Solution for Set 3 Question 10
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Solution to Question 10
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 Matias needs to borrow from the United Commercial Bank is the principal P.
How many payment periods there are is represented by N.
Because the deposit it 17 %, Matias's principal amount will be the cost of the two bedroom unit less this deposit amount:
P = 220000 - 0.01 * 17 * 220000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $182600
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 = 7.5 / 12 / 100
Monthly interest rate = 0.0063
We also need to calculate N, the total number of payments. The repayments happen every month. Matias's loan runs for 20 years, so we can calculate how many months he'll be making payments for:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0063 * 182600 / (1 - (1 + 0.0063)^(-240) )
A = $1471.01
So every month, Matias will have to pay $1471.01 to the United Commercial Bank.