Home Loan Problems Solution for Set 7 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 as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Elvis needs to borrow from the Amalgamated Bank is the principal P.
N is the number of payment periods.
Since Elvis has a 18 % deposit, the principal P for the loan is actually the price of the three bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 590000 - 0.01 * 18 * 590000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $483800
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 = 7.4 / 12 / 100
Monthly interest rate = 0.0062
We also need to calculate N, the total number of payments. Since payments occur every month, and Elvis 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 = 0.0062 * 483800 / (1 - (1 + 0.0062)^(-120) )
A = $5717.55
So every month, Elvis will have to pay $5717.55 to the Amalgamated Bank.