Home Loan Problems Solution for Set 6 Question 9
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Solution to Question 9
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 Xzavier needs to borrow from the UBS Bank USA is the principal P.
N is the number of payment periods.
Since Xzavier has a 25 % deposit, the principal P for the loan is actually the price of the flat minus this deposit amount:
[an error occurred while processing this directive]P = 430000 - 0.01 * 25 * 430000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $322500
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 = 2.4 / 12 / 100
Monthly interest rate = 0.0020
We also need to calculate N, the total number of payments. The repayments happen every month. Xzavier's loan runs for 15 years, so we can calculate how many months he'll be making payments for:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0020 * 322500 / (1 - (1 + 0.0020)^(-180) )
A = $2135.27
Finally the solution: every month, Xzavier is going to have to fork out $2135.27 to the UBS Bank USA to pay off his loan.