Question

3 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

using $5000 as the first term and increases by 5% each year, gives Value of grant = ar^n = 5000*(1.05)^10 = 5000*1.63 = 8150 $ 2) Using the formula of Sum = a(1-r^n) / (1-r), gives total grant during 2001 to 2011 = 5000(1-1.05^10) / (1-1.05) = 5000(-0.63)/(-0.05) = 63000 $ All formula applied where a is the first term, r is the ratio, and n is the (n+1)th term

Answer 2

You can apply the compound interest formula. The formula is, A = P(1+R/100)^N. where A = $ 5000, R = rate of increase per year, N = Number of years. (2011 – 2001) = 10 years.
5000 (1+5/100)^10 = 5000 (1.05)^10 = 5000 × 1.62889462675
= 5000 × 1.63 = $ 8150 given in 2011
the total amount of money given to the charity during the years 2001 to 2011 inclusive = 8150 – 5000 = $ 3150

Answer 3

using $5000 as the first term and increases by 5% each year, gives
Value of grant = ar^n
= 5000*(1.05)^10
= 5000*1.63
= 8150 $

Answer 4

where do we get 1.05?

Answer 5

how do we get r=1.05?