Home Loan Problems Solution for Set 3 Question 1
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Solution to Question 1
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 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 Dylan needs to borrow from the First Federal S&L of Charleston.
N is the number of payment periods.
Because the deposit it 13 %, Dylan's principal amount will be the cost of the two bedroom house less this deposit amount:
P = 210000 - 0.01 * 13 * 210000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $182700
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 = 9.8 / 12 / 100
Monthly interest rate = 0.0082
We also need to calculate N, the total number of payments. Since payments occur every month, and Dylan 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 = 0.0082 * 182700 / (1 - (1 + 0.0082)^(-300) )
A = $1634.51
Finally the solution: every month, Dylan is going to have to fork out $1634.51 to the First Federal S&L of Charleston to pay off his loan.