Question

If ${\left(1.05\right)}^{50}=11.6568$, then $\sum _{n=1}^{49}{\left(1.05\right)}^n$ is equal to

• A. $208.34$
• B. $213.13$
• C. $212.16$
• D. $213.16$

Answer 1

The correct option is B $213.13$

Given,${\left(1.05\right)}^{50}=11.6568$.....(1)

Now,

$\sum _{n=1}^{49}{\left(1.05\right)}^n$ $=\frac{(1.05{)}^{50}-1}{1.05-1}$

$=\frac{10.6568}{0.05}$ [ Using (1)}

$\sum _{n=1}^{49}{\left(1.05\right)}^n$$=213.13$.