Question

A collectible baseball card is predicted to increase in value by 6.5% each year. If the baseball card is worth $85 today, how many years from now will it be worth $250?

Answer 1

To determine when an $85 baseball card will reach $250 in value with a 6.5% yearly increase, use the compound interest formula. It will take approximately 14.2 years for the card to be worth $250.

Step-by-step explanation:

To find out when a collectible baseball

card worth $85 today will be worth $250 with an annual increase in value of 6.5%, we can use the formula for compound interest:

P = P0 * (1 + r)^n

Where:

P

is the future value of the card

P0

is the present value of the card

r

is the annual interest rate (expressed as a decimal)

n

is the number of years

Substituting the given values in the formula:

250 = 85 * (1 + 0.065)^n

To find

n

, we need to rearrange the formula and solve for

n

:

n = log(250/85) / log(1.065)

Calculating this gives:n ≈ 14.20

Therefore, it will take approximately 14.2 years for the baseball card to be worth $250. Since part-years cannot be accounted for in full years, you would round up to the next whole year if you're looking for the card to reach at least $250 in value.