Question
How much will Sam earn each quarter if he deposits $9,000 in a savings account with 6% interest compound quarterly? If he plans to withdraw everything at the end of the first year, will he make at least $500 in interest?
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
First quarter interest = $ Response area.
Second quarter interest = $ Response area.
Third quarter interest = $ Response area.
Fourth quarter interest = $ Response area.
Sam Response area make at least $500 in interest.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
First quarter interest = $ Response area.
Second quarter interest = $ Response area.
Third quarter interest = $ Response area.
Fourth quarter interest = $ Response area.
Sam Response area make at least $500 in interest.
Answers
GPT-4o mini
To calculate the quarterly interest earned on a $9,000 deposit with an annual interest rate of 6% compounded quarterly, we first need to determine the interest rate per quarter:
1. The annual interest rate is 6%, so the quarterly interest rate is:
\[
\frac{6\%}{4} = 1.5\% \text{ per quarter} = 0.015 \text{ (as a decimal)}
\]
2. Next, we calculate the interest earned each quarter. The formula for interest earned in a quarter is given by:
\[
\text{Interest} = \text{Principal} \times \text{Rate}
\]
#### First Quarter Interest:
- For the first quarter, the interest is:
\[
\text{Interest} = 9000 \times 0.015 = 135
\]
#### Second Quarter Interest:
- The new principal for the second quarter includes the first quarter's interest:
\[
\text{New Principal} = 9000 + 135 = 9135
\]
- Interest for the second quarter:
\[
\text{Interest} = 9135 \times 0.015 = 137.025
\]
#### Third Quarter Interest:
- New principal after second quarter:
\[
\text{New Principal} = 9135 + 137.025 = 9272.025
\]
- Interest for the third quarter:
\[
\text{Interest} = 9272.025 \times 0.015 \approx 139.080375
\]
#### Fourth Quarter Interest:
- New principal after third quarter:
\[
\text{New Principal} = 9272.025 + 139.080375 \approx 9411.105375
\]
- Interest for the fourth quarter:
\[
\text{Interest} = 9411.105375 \times 0.015 \approx 141.166580625
\]
#### Total Interest After One Year:
Now, we can sum the quarterly interest amounts to see if he will make at least $500 in interest.
- Total interest earned:
\[
\text{Total Interest} = 135 + 137.025 + 139.080375 + 141.166580625 \approx 552.271955625
\]
This is greater than $500, so Sam will indeed make at least $500 in interest.
### Final Responses:
1. First quarter interest = **$135**
2. Second quarter interest = **$137.03**
3. Third quarter interest = **$139.08**
4. Fourth quarter interest = **$141.17**
5. Sam will make at least $500 in interest = **Yes**
1. The annual interest rate is 6%, so the quarterly interest rate is:
\[
\frac{6\%}{4} = 1.5\% \text{ per quarter} = 0.015 \text{ (as a decimal)}
\]
2. Next, we calculate the interest earned each quarter. The formula for interest earned in a quarter is given by:
\[
\text{Interest} = \text{Principal} \times \text{Rate}
\]
#### First Quarter Interest:
- For the first quarter, the interest is:
\[
\text{Interest} = 9000 \times 0.015 = 135
\]
#### Second Quarter Interest:
- The new principal for the second quarter includes the first quarter's interest:
\[
\text{New Principal} = 9000 + 135 = 9135
\]
- Interest for the second quarter:
\[
\text{Interest} = 9135 \times 0.015 = 137.025
\]
#### Third Quarter Interest:
- New principal after second quarter:
\[
\text{New Principal} = 9135 + 137.025 = 9272.025
\]
- Interest for the third quarter:
\[
\text{Interest} = 9272.025 \times 0.015 \approx 139.080375
\]
#### Fourth Quarter Interest:
- New principal after third quarter:
\[
\text{New Principal} = 9272.025 + 139.080375 \approx 9411.105375
\]
- Interest for the fourth quarter:
\[
\text{Interest} = 9411.105375 \times 0.015 \approx 141.166580625
\]
#### Total Interest After One Year:
Now, we can sum the quarterly interest amounts to see if he will make at least $500 in interest.
- Total interest earned:
\[
\text{Total Interest} = 135 + 137.025 + 139.080375 + 141.166580625 \approx 552.271955625
\]
This is greater than $500, so Sam will indeed make at least $500 in interest.
### Final Responses:
1. First quarter interest = **$135**
2. Second quarter interest = **$137.03**
3. Third quarter interest = **$139.08**
4. Fourth quarter interest = **$141.17**
5. Sam will make at least $500 in interest = **Yes**