Respuesta :
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
[tex]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}}[/tex]
[tex]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}}[/tex]
=$126,964.34
Learn more about present value:
https://brainly.com/question/17322936
#SPJ4
