Question

Sally puts $1,300 into an account earning 2% simple interest. How long will she need to wait before her money is doubled?

43 years
37 years
33 years
50 years

Answer 1

To determine how long it will take for Sally's money to double with simple interest, we can use the formula for simple interest:

\[ A = P(1 + rt) \]

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 rate of interest per year (decimal).
- \( t \) is the time the money is invested for in years.

Since Sally wants her money to double, we want:

\[ A = 2P \]

Given:
- \( P = 1300 \)
- \( r = 0.02 \)

We can plug these into the formula, setting \( A = 2 \times 1300 = 2600 \):

\[
2600 = 1300(1 + 0.02t)
\]

Now, simplify the equation:

1. Divide both sides by 1300:
\[
2 = 1 + 0.02t
\]

2. Subtract 1 from both sides:
\[
1 = 0.02t
\]

3. Divide both sides by 0.02:
\[
t = \frac{1}{0.02} = 50
\]

Thus, it will take Sally **50 years** for her money to double.

The answer is: **50 years**.