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%.