Question

Each year a company gives a grant to a charity. The amount given each year increases by 5% of its
value in the preceding year. The grant in 2001 was $5000. Find
(i) the grant given in 2011, [3]
(ii) the total amount of money given to the charity during the years 2001 to 2011 inclusive. [2]

Answer 1

\(\Large \color{purple}{5000(1 + {5\over100})^{n} }\)
Use this formula.

Answer 2

For the second part:

Total = 5000 + 5000(1.05) + 5000(1.05)^2 + ... + 5000(1.05)^10

Let 1.05 = x

Total = 5000 + 5000x + 5000x^2 + ... + 5000x^10

-> Total = 5000(1 + x + x^2 + ... + x^10)
Total * x = 5000(x + x^2 + ... + x^11)

xTotal - Total = 5000(x^11 - 1)

Total = 5000[(x^11 - 1)/(x - 1)]

\[Total =5000[ {1.05^{11} -1 \over 1.05 - 1}]\]

Answer 3

thanks guys :)