Home Loan Problems Solution for Set 2 Question 1
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Solution to Question 1
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 Howard needs to borrow from the First Federal Bank of Calif..
How many payment periods there are is represented by N.
Since Howard has a 30 % 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 = 290000 - 0.01 * 30 * 290000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $203000
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 = 3.4 / 12 / 100
Monthly interest rate = 0.0028
We also need to calculate N, the total number of payments. Since payments occur every month, and Howard 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 = 0.0028 * 203000 / (1 - (1 + 0.0028)^(-120) )
A = $1997.87
So every month, Howard will have to pay $1997.87 to the First Federal Bank of Calif..