Home Loan Problems Solution for Set 6 Question 2
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Solution to Question 2
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 expressed as a decimal (NOT A PERCENTAGE!), for the period of time over which payments are made.
The amount that Jefferson needs to borrow from the Banco Popular de Puerto Rico is the principal P.
How many payment periods there are is represented by N.
Since Jefferson has a 7 % deposit, the principal P for the loan is actually the price of the one bedroom unit minus this deposit amount:
[an error occurred while processing this directive]P = 160000 - 0.01 * 7 * 160000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $148800
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 = 6.9 / 12 / 100
Monthly interest rate = 0.0058
We also need to calculate N, the total number of payments. The repayments happen every month. Jefferson's loan runs for 30 years, so we can calculate how many months he'll be making payments for:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0058 * 148800 / (1 - (1 + 0.0058)^(-360) )
A = $980.00
So every month, Jefferson will have to pay $980.00 to the Banco Popular de Puerto Rico.