Question 1206512: Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $10,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10%; it calls for payments every 6 months, beginning on June 30th, and is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the second mortgage was for 10,000 at 10% nominal interest per year compounded semi-annually, beginning on june 30th.
in one year, she made two payments at the end of each semi-annual period at 10/2 = 5% per semi-annual period.
at the beginning of the first semi-annual period, she owes 10,000.
the loan is for 10 years, so her semi-annual payment is calculated to be 802.4258719 = 802.43 when rounded to 2 decimal places.
the interest for the first two semi-annual periods are calculated as follows:
loan is 10,000
at the end of the first semi-annual period, the remaining balance becomes 10,000 * 1.05 = 10,500.
the interest on that is 10,500 minus 10,000 = 500.
the first payment of 802.4258719 is made.
this reduces the remaining balance to 10,500 minus 802.4258719 = 9697.5741281 = 9697.57 when rounded to 2 decimal places.
at the end of the second semi-annual period, the remaining balance becomes 9697.5741281 * 1.05 = 10182.45283.
the interest on that is 10182.45283 minus 9697.5741281 = 484.8787065.
the second payment 802.4258719 is made.
this reduces the remaining balance to 10182.45283 minus 802.4258719 = 9380.026963 = 9380.03 when rounded to two decimal places.
this process continue for 10 years until the loan is paid off.
the interest that she paid for the first two semi-annual periods is 500 + 484.88 = 984.88, rounded to the nearest penny.
round that to the nearest dollar and you get 985.
each semi-annual time period calculation, shown below.
the time periods of interest to you are the time periods from 0 to 2.
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