A computer is worth $2000 when it is new. After each year it is worth half what it was the previous year. What will its worth be after 5 years?

1 Answer
Jan 1, 2016

It's a simple geometric progression of ratio r = 1/2r=12

Explanation:

After the first year, the value will be given by:

V_1 =$2000*(1/2)=$1000V1=$2000(12)=$1000

In the second:

V_color(red)(2)=V_1*(1/2)=$2000*color(red)((1/2)*(1/2))=$2000*color(red)((1/2)^2)=500V2=V1(12)=$2000(12)(12)=$2000(12)2=500

In the n^(th)nth year:

V_color(red)(n)=$2000*(1/2)^color(red)(n)Vn=$2000(12)n

So, after 5 years:

V_5=$2000*(1/2)^5=$2000*(1/32)=($2000)/32=$62.50V5=$2000(12)5=$2000(132)=$200032=$62.50