Question

On a 15-year, $200K mortgage at 4% APR, how much interest will you pay in ONLY the second year if you make the regular monthly payments?

Multiple Choice

• $8,366

• $17,170

• $1,497

• $680

• $9,083

Answer 1

Ans) On a 15 year, $200k or $2,00,000 mortgage at 4% APR(annual Percentage rate), pay in the second year is to be found.

4% APR = 4%/12 => 0.34% monthly rate or .0034 monthly.

Payment till the 1st year would be payment for 12 months, similarly payment till 2nd year would be payment for 24 months.

Now, in order to find payment for the 2nd year only we have to find the payment from 13th month to 24th month,

It can be found out by finding out the payment till 2nd yr i.e. 24th month and subtracting from it payment for 1st year i.e. 12 months. it is calculated in the following way:

24 month compounded amount - 12 month compunded amount = Interest in the 2nd year

=> 2,00,000 ( 1 + .0034)^24 - 2,00,000( 1 + .0034)^12 = Interest in the 2nd year

=> 2,00,000 * 1.084 - 2,00,000 * 1.0415 = Interest in the 2nd year

=> 216800 - 208300 =Interest in the 2nd year  

=> 8500 approx. (such discrepancies could arise in rounding off)

Therefore, option a) $8366 will be the interest in the 2nd year only.