Home Loan Problems Solution for Set 8 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.
The amount that Kamren needs to borrow from the Chase Bank USA is the principal P.
How many payment periods there are is represented by N.
Since Kamren has a 6 % deposit, the principal P for the loan is actually the price of the one bedroom apartment minus this deposit amount:
P = 340000 - 0.01 * 6 * 340000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $319600
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 = 10.2 / 12 / 100
Monthly interest rate = 0.0085
We also need to calculate N, the total number of payments. Since payments occur every month, and Kamren has a 25 year loan:
N = 12 * 25
N = 300
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0085 * 319600 / (1 - (1 + 0.0085)^(-300) )
A = $2949.39
So every month, Kamren will have to pay $2949.39 to the Chase Bank USA.