Home Loan Problems Solution for Set 4 Question 8
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Solution to Question 8
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 Peyton needs to borrow from the Banco Bilbao Vizcaya Argentaria is the principal P.
N is the number of payment periods.
Since Peyton has a 7 % deposit, the principal P for the loan is actually the price of the three bedroom flat minus this deposit amount:
[an error occurred while processing this directive]P = 500000 - 0.01 * 7 * 500000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $465000
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 = 5.6 / 12 / 100
Monthly interest rate = 0.0047
We also need to calculate N, the total number of payments. Since payments occur every month, and Peyton has a 15 year loan:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0047 * 465000 / (1 - (1 + 0.0047)^(-180) )
A = $3824.15
So every month, Peyton will have to pay $3824.15 to the Banco Bilbao Vizcaya Argentaria.