Question
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?
a.
6 percent
b.
7 percent
c.
5 percent
d.
8 percent
a.
6 percent
b.
7 percent
c.
5 percent
d.
8 percent
Answers
GPT-4o mini
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 \( \text{(b) } 7 \text{ percent} \).
\[
A = P(1 + r)
\]
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 \( \text{(b) } 7 \text{ percent} \).