Question

It is predicted that garden gnome value will go up by 2% each year, forming a geometric progression. Jean-Claude has a garden gnome currently valued at £80,000. If the rate of inflation is correct:

a) What will Jean-Claude's gnome be worth after 1 year?


b) What is the common ratio of the geometric progression?


c) What will Jean-Claude's gnome be worth after 10 years?


d) It will take k years for the value of Jean-Claude's gnome to exceed £120,000. Find k.

Answer 1

Explanation:

a ) The worth of Jean-Claude's gnome after 1 year

= 80000 x 1.02

= £81600

b ) common ratio of geometric progression

= 81600 / 80000

= 1.02

c ) worth after 10 years

= 80000 x 1.02¹⁰

= 80000 x 1.21899

= £97519.55

d )

120000 = 80000 x
`1.02^k`

1.5 =
`1.02^k`

ln1.5 = k ln 1.02

k = ln 1.5 / ln 1.02

= .4054 / .0198

= 20.47 years .