10% increase on an item and you purchased one every year for 100 years how much would you spend.total.

Question

If an item was say worth $20 and you purchased it this year and next year it had gone up by 10% it would now be worth $22.

If you bought this one at $22 as well as the first one foe $20 you would have spent a total of $42 dollars.

How would you calculate this 2 year example for 100 years?

Answer 1

20+22 =42

20+22+24.2 = 66.2

this problem involves finding the sum of a geometric series

with first term, a1,=20 and common ratio = 1.1

each term is 1.1 times the preceding term

20+22+24.2+26.62 = 92.82

a1=20

a2=20(1.1)=22

a3=20(1.1)^2 = 24.2

a4 =20(1.1)^3 = 92.82

an=a1(r)^(n-1)

an=20(1.1)^(n-1)

a100=20(1.1)^99

sn = sum of a1 through a100

sn = a1(1-r^n)/(1-r)

=a1(r^n-1)/(r-1)

s100=20(1.1^100-1)/(1.1-1)

= 20(1.1^100-1)/.1

= 200(1.1^100-1)

=2,756,122.468-200

=$2,755,922.468 after 100 years