Question

Ten years ago a collector paid $2,000 for a Cal Ripkin autographed

baseball. Today it is worth $24,000. Find the annual rate of appreciation

Answer 1

Given:

Given that ten years ago a collector paid $2000 for a Cal Ripkin autographed baseball. Today it is worth $24,000.

We need to determine the annual rate of appreciation.

Rate of appreciation:

The rate of appreciation can be determined using the formula,

`r=100[((A)/(P))^{(1)/(t)}-1]`

where A is the total amount,

P is the initial amount,

t is the time in years and

r is the rate of appreciation.

Substituting A = 24,000, P = 2000 and t = 10, we get;

`r=100[((24000)/(2000))^{(1)/(10)}-1]`

Simplifying, we get;

`r=100[(12)^{(1)/(10)}-1]`

`r=100[(1.28209)-1]`

`r=100(0.28209)`

`r=28.209 \%`

Thus, the rate of appreciation is 28.209%