Tim put $275 in the bank one year ago and forgot about it. Today, the bank sent Tim a statement indicating that he now has $294.25 in his account. What interest rate did Tim earn?

Question

a.

6 percent
b.

7 percent
c.

5 percent
d.

8 percent

Answer 1

To find the interest rate that Tim earned on his savings, we can use the formula for simple interest, which is:

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

Where:

• \( A \) is the amount of money accumulated after one year (the ending balance),
• \( P \) is the principal amount (the initial investment),
• \( r \) is the interest rate (as a decimal).

In this case, we have:

• \( A = 294.25 \)
• \( P = 275 \)

We need to solve for \( r \):

\[ 294.25 = 275(1 + r) \]

To isolate \( r \), first divide both sides by 275:

\[ \frac{294.25}{275} = 1 + r \]

Calculating the left side:

\[ \frac{294.25}{275} \approx 1.069818 \]

Now subtract 1 from both sides to find \( r \):

\[ r \approx 1.069818 - 1 \approx 0.069818 \]

Convert \( r \) to a percentage:

\[ r \times 100% \approx 6.98% \]

Rounding to the nearest whole number gives us approximately \( 7% \).

Therefore, the correct answer is \( \text{(b) } 7 \text{ percent} \).