To model the situation where your initial amount, \( P \), increases at a rate of \( r \) (in this case, 2% or 0.02) each year, you can use the formula for compound interest:
\[ A(t) = P(1 + r)^t \]
Where:
- \( A(t) \) is the amount of money in the account after \( t \) years,
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the rate of interest (as a decimal),
- \( t \) is the number of years.
Given:
- \( P = 2500 \)
- \( r = 0.02 \)
The function modeling the situation will be:
\[ A(t) = 2500(1 + 0.02)^t \]
or simplified:
\[ A(t) = 2500(1.02)^t \]
To find out how much money you will have in 3 years, substitute \( t = 3 \) into the function:
\[ A(3) = 2500(1.02)^3 \]
Now, calculate \( (1.02)^3 \):
\[ (1.02)^3 \approx 1.061208 \]
Now calculate \( A(3) \):
\[ A(3) = 2500 \times 1.061208 \approx 2653.02 \]
In 3 years, the account will have approximately $2,653.02.