Question 1206658: Starting on July 1, 2000, Peter borrows $7600
each year for 4 years from his dear Aunt May to pay for college. (Note: the last date that he borrows money is July 1, 2003.) From the beginning, Aunt May agreed to defer all interest on the loans until Peter finds a job; i.e. Peter's loans will not accumulate any interest until the first day he starts working. After that, Peter will be charged 8 percent compounded semiannually, and he will pay Aunt May back with 14 equal semiannual payments, the first coming 6 months after he starts his job. Peter finds a job as a photographer for a local newspaper, and his first day of work is July 1, 2004. For tax reasons, Peter needs to compute the total amount of interest that he will pay to Aunt May in the year 2007. How much in interest did Peter actually pay in 2007?
Answer by ikleyn(52878)   (Show Source):
You can put this solution on YOUR website! .
1206658
Starting on July 1, 2000, Peter borrows $7600 each year for 4 years from his dear Aunt May
to pay for college. (Note: the last date that he borrows money is July 1, 2003.)
From the beginning, Aunt May agreed to defer all interest on the loans until Peter finds a job;
i.e. Peter's loans will not accumulate any interest until the first day he starts working.
After that, Peter will be charged 8 percent compounded semiannually,
and he will pay Aunt May back with 14 equal semiannual payments,
the first coming 6 months after he starts his job.
Peter finds a job as a photographer for a local newspaper, and his first day of work is July 1, 2004.
For tax reasons, Peter needs to compute the total amount of interest that he will pay to Aunt May
in the year 2007. How much in interest did Peter actually pay in 2007?
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Let's make the timeline
July 1, 2000 Peter borrows $7600 The debt becomes $7600
July 1, 2001 Peter borrows $7600 The debt becomes $15200
July 1, 2002 Peter borrows $7600 The debt becomes $22800
July 1, 2003 Peter borrows $7600 The debt becomes $30400
July 1, 2004 Peter found the job The debt is $30400 and Peter is charged 8% compounded semiannually from this date
So, starting from July 1, 2004 we have classic loan problem:
the loan amount is $30400; it is 8% charged semiannually;
the debt should be repaid in 14 equal semiannual payments (two payments per year),
in 7 years (2005, 2006, 2007, 2008, 2009, 20010, 2011).
Make one more timeline
1-st payment Jan 1, 2005 first payment comes 6 months after he starts his job
2-nd payment Jul 1, 2005
3-rd payment Jan 1, 2006
4-th payment Jul 1, 2006
5-th payment Jan 1, 2007
6-th payment Jul 1, 2007
They want you determine the total amount of interest Peter pays in 2007.
So, they want you find the sum of the interest portions of the 5-th and 6-th payments.
Use the Excel function IPMT, which is specially designed to calculate the interest part
of a classic loan scheme for the specific payments.
For description of this function see these sources
wording/text description
https://www.wallstreetprep.com/knowledge/ipmt-function/
Youtube videos
https://www.youtube.com/watch?v=xZq4RNqE7ts
https://www.youtube.com/watch?v=bni0l75lc-8
The format of the function IPMT is as follows
= IPMT(rate, per, nper, principal, fv, type)
In this format "rate" is the rate per period = 0.04 (= 0.08/2 semiannually) required parameter
per = 5 - the payment, of which we want to get the interest part; required parameter
nper = 14 - total number of payments; required parameter
principal = 30400; required parameter
fv is optional (we can omit it);
type is optional (we can omit it, which means that
the payment is due at the end of the half-year period)
So, we write in Excel cell/spreadsheet for the interest part of the 5-th payment
= IPMT(0.04, 5, 14, 30400), and we get the value of the interest for the 5-th payment of $933.71.
Next, we write in Excel cell/spreadsheet for the interest part of the 6-th payment
= IPMT(0.04, 6, 14, 30400), and we get the value of the interest for the 6-th payment of $855.64.
So, total interest part of the two Peter's payments of the year 2007 is the sum $933.71 + $855.64 = $1,789.64. ANSWER
Solved.
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