Question

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

Answer 1

To find out how long it will take for Sally's money to double when earning simple interest, we can use the simple interest formula:

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

where:
- \( A \) is the amount of money accumulated after time \( t \),
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (in decimal),
- \( t \) is the time in years.

Sally wants her money to double, so \( A = 2P \).

Given:
- \( P = 1300 \)
- \( r = 0.02 \) (2% as a decimal)

We want to find \( t \) when \( A = 2 \times 1300 = 2600 \).

Substituting into the formula, we have:

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

Dividing both sides by 1300:

\[
2 = 1 + 0.02t
\]

Subtracting 1 from both sides:

\[
1 = 0.02t
\]

Now divide by 0.02:

\[
t = \frac{1}{0.02} = 50
\]

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

The correct answer is **50 years**.