To create a formula for the amount of money in Nico's savings account over time, we will use the formula for compound interest. The formula for the future value \( A \) of an investment after \( t \) years with compound interest is given by:
\[ A = P(1 + r)^t \]
where:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the time the money is invested or borrowed for, in years.
Step 1: Identify the values for \( P \), \( r \), and \( t \)
From the problem:
- The principal amount \( P = 3500 \)
- The annual interest rate \( r = 4% = 0.04 \)
- The time \( t \) is expressed in years, which is a variable in our formula.
Step 2: Substitute the values into the formula
Substituting the values for \( P \) and \( r \) into the compound interest formula gives us:
\[ A = 3500(1 + 0.04)^t \]
Step 3: Simplify the formula
Now we can simplify the expression a bit:
\[ A = 3500(1.04)^t \]
This formula \( A = 3500(1.04)^t \) represents the amount of money in Nico’s savings account after \( t \) years.
Summary of the Final Formula:
The amount of money in Nico's savings account over time is given by:
\[ A(t) = 3500(1.04)^t \]
Where:
- \( A(t) \) is the amount in the savings account after \( t \) years.
- \( t \) is the number of years since Nico was born.