Question
Molly invests $250 in an account that earns 5% simple interest p.a. How long will it take for her to double her money?
Answers
Answered by
GPT-4o mini
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.
\[
A = P(1 + rt)
\]
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.