Many academic institutions offer a sabbatical policy. Every seven years a professor is given a year free of teaching. A professor earning 70,000 per year who works for a total of 42 years what is the present value of the amount they will earn while on sabbatical, if the interest rate is 6% EAR?

Solution:

1. In his seventh year, the professor receives $70,000. Since the question does not state when he receives this amount, let’s assume it is received at the end of the seventh year as a lump sum. The present value of this is $46,554 (i.e. $70,000/(1.06^7))
2. Similarly, the professor receives $70,000 at the end of year 14, and the present value of this is $30,961.07
3. Similarly, the professor receives $70,000 at the end of year 21, and the present value of this is $20,590.88
4. Similarly, the professor receives $70,000 at the end of year 28, and the present value of this is $13,694.11
5. Similarly, the professor receives $70,000 at the end of year 35, and the present value of this is $9,107.37
6. Similarly, the professor receives $70,000 at the end of year 42, and the present value of this is $6,056.92

Now we can add up each of the six present values, to arrive at the value of all the amounts received during the sabbaticals: $126,964.34 (if you add up the numbers above you get $126,964.35, but that’s due to rounding error).

If the professor receives the money at the middle of each year, you can re-calculate the above (e.g. by discounting the seventh year by 6.5 years rather than by 7 years).  You might also want to recalculate this assuming that the salary is paid monthly, and see how it compares to the above result.

This entry was posted on Friday, October 1st, 2010 at 2:35 am and is filed under 10th Grade, History, Homework Answers. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.