18. a rare coin is worth $250. the coin increases in value by 10% each year. what will the coin be worth in…

18. a rare coin is worth $250. the coin increases in value by 10% each year. what will the coin be worth in 12 years?

18. a rare coin is worth $250. the coin increases in value by 10% each year. what will the coin be worth in 12 years?

Answer

Explanation:

Step1: Identify the compound - growth formula

The formula for compound - growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the rate of growth as a decimal, and $t$ is the number of time periods. Here, $P=$250$, $r = 0.1$ (since 10%=0.1), and $t = 12$.

Step2: Substitute the values into the formula

$A=250\times(1 + 0.1)^{12}$. First, calculate $(1 + 0.1)^{12}$. $(1.1)^{12}\approx3.13842837672$. Then, multiply by the initial value. $A = 250\times3.13842837672$. $A\approx784.61$.

Answer:

$$784.61$