The value of a rare baseball card increases by 29% each year. If Andrew bought the baseball card for $150, how much will it be worth after 6 years?
Future Amount = [tex]I(1+r)^t[/tex]
$[?]
Round to the nearest whole number.
Answer (2)
Identify the initial value, rate of increase, and time period: I = $150 , r = 0.29 , t = 6 .
Substitute the values into the future value formula: Future Amount = 150 ( 1 + 0.29 ) 6 .
Calculate the future amount: Future Amount = 150 ( 1.29 ) 6 ≈ 691.24 .
Round to the nearest whole number: The baseball card will be worth approximately 691 dollars after 6 years.
Explanation
Understanding the Problem We are given that the initial value of the baseball card is $150, and it increases by 29% each year. We want to find its value after 6 years. The formula for the future value is given by:
Future Amount = I ( 1 + r ) t
where I is the initial amount, r is the rate of increase, and t is the time in years.
Identifying the Values We have the following values:
Initial value, I = $150 Rate of increase, r = 29% = 0.29 Time period, t = 6 years
Substituting the Values Now, we substitute these values into the formula:
Future Amount = 150 ( 1 + 0.29 ) 6
Future Amount = 150 ( 1.29 ) 6
Calculating the Future Amount Calculating the future amount:
Future Amount = 150 × ( 1.29 ) 6 ≈ 150 × 4.60827366 ≈ 691.241049
Rounding this to the nearest whole number, we get 691.
Final Answer Therefore, the baseball card will be worth approximately $691 after 6 years.
Examples
Imagine you bought a rare collectible item, like a limited-edition comic book, for $150. If its value increases by 29% each year, this formula helps you estimate its worth after several years. This is similar to how investments grow over time with a certain rate of return. Understanding exponential growth can help you make informed decisions about investments and savings, projecting their future value based on consistent growth rates.
After calculating the future value of Andrew's baseball card using the formula for exponential growth, we find it will be worth approximately $743 after 6 years.
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