Question

# You bought a house for 150,000.  The bank required a 20% down payment and gave you a...

You bought a house for 150,000.  The bank required a 20% down payment and gave you a 30-year mortgage loan for the remainder.  Assume an annual interest rate of 3.5% and a monthly repayment schedule.  What is your monthly payment?  After 18 years of payments, how much do you still owe?

Value of House = \$150,000

Down Payment = 20% of \$150,000 = \$150,000 * 0.20 = \$30,000

Loan Amount = \$150,000 - \$30,000 = \$120,000

Tenure = 30 Years

No of installments = 30 *12 = 360

Annual Rate = 3.5%

rate per month = 3.5 /(12 *100) = 0.00292

Monthly Payment = [loan amount * rate per month * (1 + rate per month) ^ no of installments] / [ (1 + rate per month) ^ no of installments - 1]

= [ \$120,000 * 0.00292 * ( 1 + 0.00292) ^ 360] / [ ( 1 + 0.00292) ^ 360 -1]

= [ \$120,000 * 0.00292 * 2.8567] / [ 2.8567 -1 ]

= \$539.12

Principal outstanding = loan amount * (1 + rate per month) ^ no of payments - [ monthly payment * { (1+ rate per month) ^ no of payment -1} / rate per month]

= \$120,000 * (1 + 0.00292) ^216 - [ \$539.12 * { ( 1 + 0.00292) ^216 - 1} / 0.00292]

= \$120,000 * 1.8772 - [\$539.12 * 0.8772 / 0.00292]

= \$225,264 - \$161,957.56

=\$63,306.44

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