To determine how long it will take for Molly to double her investment of $250 at a simple interest rate of 5% per annum, we can use the formula for simple interest:
\[ A = P(1 + rt) \]
Where:
- \( A \) is the amount of money accumulated after time \( t \) (the final amount).
- \( P \) is the principal amount (the initial investment).
- \( r \) is the annual interest rate (in decimal form).
- \( t \) is the time the money is invested for in years.
Molly wants to double her money, so we set \( A = 2P \):
\[ 2P = P(1 + rt) \]
We can simplify this by dividing both sides by \( P \) (assuming \( P \neq 0 \)):
\[ 2 = 1 + rt \]
Subtracting 1 from both sides gives:
\[ 1 = rt \]
Now we can substitute \( r = 0.05 \) (5% expressed as a decimal):
\[ 1 = 0.05t \]
To find \( t \), divide both sides by 0.05:
\[ t = \frac{1}{0.05} = 20 \]
Thus, it will take Molly 20 years to double her investment.