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.

Explanation:

Identify given values

For Lindsey:

• Principal \(P_L = \$250\)
• Time \(t_L = 1\text{ year}\)
• Balance \(A_L = \$253\)

For Jenn:

• Principal \(P_J = \$250\)
• Time \(t_J = 2\text{ years}\)
• Balance \(A_J = \$257.50\)

Calculate Lindsey's interest rate

Find interest earned:

$$I_L = A_L - P_L = 253 - 250 = \$3$$

Use simple interest formula \(I = P \cdot r \cdot t\):

$$3 = 250 \cdot r_L \cdot 1$$

$$r_L = \frac{3}{250} = 0.012 = 1.2\%$$

Calculate Jenn's interest rate

Find interest earned:

$$I_J = A_J - P_J = 257.50 - 250 = \$7.50$$

Use simple interest formula \(I = P \cdot r \cdot t\):

$$7.50 = 250 \cdot r_J \cdot 2$$

$$7.50 = 500 \cdot r_J$$

$$r_J = \frac{7.50}{500} = 0.015 = 1.5\%$$

Compare the interest rates

Compare the rates:

$$1.5\% > 1.2\%$$

Jenn's rate is higher.

Answer:

Jenn's account has the greater simple interest rate. Lindsey's simple interest rate is \(1.2\%\), while Jenn's simple interest rate is \(1.5\%\).