Home Loan Problems Solution for Set 6 Question 10
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Solution to Question 10
The equation you need to use is as follows:
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.
P is the principal - this is the amount that Todd needs to borrow from the Wachovia Bank.
How many payment periods there are is represented by N.
Since Todd has a 24 % deposit, the principal P for the loan is actually the price of the flat minus this deposit amount:
P = 430000 - 0.01 * 24 * 430000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $326800
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 6.0 / 12 / 100
Monthly interest rate = 0.0050
We also need to calculate N, the total number of payments. Since payments occur every month, and Todd 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 = 0.0050 * 326800 / (1 - (1 + 0.0050)^(-180) )
A = $2757.73
Finally the solution: every month, Todd is going to have to fork out $2757.73 to the Wachovia Bank to pay off his loan.