Question

A tree increases annually by 1/8 th of its height. by how much will it increase after 2(1/2) years, if it stand today 10 ft. high?

Answer 1

 Time = 21/2 years , R % = 1/8×100⇒25/2 %
A = P {[ 1+R/100 ]n× [ 1+R/100 ]}
A = P{[ 1+25/100×2 ]^2 × [ 1+ 25/100×2×2 ] }
A = 10×81/64×17/16 
A = 13.77

Answer 2

Increase in 1 year = 1/8 th
Increase in 2 years = 2/8 th = 1/4 th
Increase in 2 1/2 years = (1/4 + (1/8 x 1/2))th
Increase in 2 1/2 years = (1/4 + 1/16)th
Increase in 2 1/2 years = (4/16 + 1/16)th
Increase in 2 1/2 years = 5/16th

So after 2 1/2 years is =
Height of tree today + ( Increase x Height of tree today )
=10 + ( 5 x 10 ) / 16
= 10 + 3.125
= 13.125 ft