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.

Please show work thank you !

Answer 1

This is a geometric progression with first term (a) as d/(1+k) and common ratio (r) as (1+g)/(1+k) and number of terms (n) as n+1

The sum for n+1 terms is a*(1-r^(n+1))/(1-r)

Here sum will be d/(1+k)*(1-((1+g)/(1+k))^(n+1))/(1-(1+g)/(1+k))=8/1.07*(1-(1.03/1.07)^11)/(1-(1.03/1.07))=68.4721