Question

Suppose $LaTeX: S=\frac{d}{1+k}+\frac{d(1+g)}{(1+k)^2}+\frac{d(1+g)^2}{(1+k)^3}+...+\frac{d(1+g)^n}{(1+k)^{n+1}}$ , obtain the value of S if d=8, g=0.03, k=0.07, and n=10. Round your final answer to two decimal places.

Answer 1

Answer:

To get value of S, we can use the formula to get Present value of growing annuity:

S = PV = [d / (k - g)] * [1 - {(1 + g) / (1 + k)} ^{n +1}]

= (8 /(7% - 3%)) * (1 - ((1 + 3%) / (1 + 7%)) ¹¹)

= $68.47209

= $68.47

Value of S = $68.47

Alternately this can be done in excel as follows: