Question

According to the Original Tooth Fairy Poll sponsored by Delta Dental, the average payout per tooth by the Tooth Fairy was $1.50 in 2000. In 2017, the payment per tooth went up to $4.66.[1] What has been the average annual growth rate of Tooth Fairy payment from 2000 to 2017? The S&P index value in 2000 is 1360.16,[2] and the index value is 2294.69 in 2017.[3] What has been the average annual growth rate of the S&P 500 from 2000 to 2017?

Answer 1

We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

a.4.66=1.5*(1+r/100)^17

(4.66/1.5)^(1/17)=(1+r/100)

(1+r/100)=1.069

r=1.069-1

=6.9%(Approx)

b.2294.69=1360.16*(1+r/100)^17

(2294.69/1360.16)^(1/17)=(1+r/100)

(1+r/100)=1.0312

r=1.0312-1

=3.12%(Approx)