Question

many academic institutions offer a sabbatical policy. every seven years a professor is given a year free of teaching and other administrative responsibilities at full pay. for a professor earning $70,000 per year who works for a total of 42 years, what is the present value of the amount she will earn while on sabbatical if t

Answer 1

Present value of the amount she will earn while on sabbatical if the interest rate is 6% is $126,964.34

The value of money reduces as time passes, this is due to the interest factor. $1 is worth more today than tomorrow this is because of the time value of money. The present value of cash flows is discounted value of future cash flows. Discount factors at a given rate of interest are used to find out the present value of cash flows.

Here, the professor will receive $70,000 every 7 years for 42 years.

Hence he will receive $70,000 sabbatical in the 7th, 14th,21st,28th,35th, and 42nd years.

We will find the present value of such receipts and add them.

R=0.06

F=$70,000

$Present~Value = \displaystyle\frac{FV}{(1+r)^7}+\frac{FV}{(1+r)^{14}}+\frac{FV}{(1+r)^{21}}+\frac{FV}{(1+r)^{28}}+\frac{FV}{(1+r)^{35}}+\frac{FV}{(1+r)^{42}}$

$Present~Value = \displaystyle\frac{70,000}{(1.06)^7}+\frac{70,000}{(1.06)^{14}}+\frac{70,000}{(1.06)^{21}}+\frac{70,000}{(1.06)^{28}}+\frac{70,000}{(1.06)^{35}}+\frac{70,000}{(1.06)^{42}}$

=$126,964.34

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