Question

One year ago, Lindsey deposited $250 into a savings account. Her balance is now $253. Two years ago, Jenn deposited $250 into a savings account. Her balance is now $257.50. Which account has the greater simple interest rate? Explain.

Answer 1

To determine which account has the greater simple interest rate, we can use the formula for simple interest:

\[
\text{Simple Interest} = P \times r \times t
\]

where:
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time in years.

We can also rearrange this formula to find the interest rate:

\[
r = \frac{\text{Simple Interest}}{P \times t}
\]

### Calculating for Lindsey

1. **Principal (P)**: $250
2. **Final Balance**: $253
3. **Time (t)**: 1 year
4. **Simple Interest (I)**: Final Balance - Principal = $253 - $250 = $3

Now we can calculate the interest rate:

\[
r = \frac{I}{P \times t} = \frac{3}{250 \times 1} = \frac{3}{250} = 0.012
\]

Converting to percentage:

\[
r = 0.012 \times 100\% = 1.2\%
\]

### Calculating for Jenn

1. **Principal (P)**: $250
2. **Final Balance**: $257.50
3. **Time (t)**: 2 years
4. **Simple Interest (I)**: Final Balance - Principal = $257.50 - $250 = $7.50

Now we can calculate the interest rate:

\[
r = \frac{I}{P \times t} = \frac{7.50}{250 \times 2} = \frac{7.50}{500} = 0.015
\]

Converting to percentage:

\[
r = 0.015 \times 100\% = 1.5\%
\]

### Conclusion

- Lindsey's account interest rate: 1.2%
- Jenn's account interest rate: 1.5%

Therefore, **Jenn's account has the greater simple interest rate** of 1.5% compared to Lindsey's rate of 1.2%.