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,
[tex]r=100[(\frac{A}{P})^{\frac{1}{t}}-1][/tex]
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;
[tex]r=100[(\frac{24000}{2000})^{\frac{1}{10}}-1][/tex]
Simplifying, we get;
[tex]r=100[(12)^{\frac{1}{10}}-1][/tex]
[tex]r=100[(1.28209)-1][/tex]
[tex]r=100(0.28209)[/tex]
[tex]r=28.209 \%[/tex]
Thus, the rate of appreciation is 28.209%
