Question:

Each year a company gives a grant to a charity. The amount given each year increases by $\displaystyle 5\%$ of its value in the preceding year. The grant in 2001 was $\displaystyle \$5000$. Find:

(i) the grant given in 2011,

(ii) the total amount of money given to the charity during the years 2001 to 2011 inclusive.

Attempt:

$\displaystyle a = \$5000$

$\displaystyle r = 5\% = 0.05$

$\displaystyle 2001 \rightarrow 2011 = 10 years$

$\displaystyle U_{11} = a.r^{10}$

$\displaystyle U_{11} = 5000 \times 0.05^{10} = 4.88^{-10}$

I don't think that is possible ! How can I solve this question?