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 = $ 135.
Second quarter interest = $ Response area.
Third quarter interest = $ Response area.
Fourth quarter interest = $ Response area.
Sam will make at least $500 in interest.
606.74139.08141.17
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 = $ 135.
Second quarter interest = $ Response area.
Third quarter interest = $ Response area.
Fourth quarter interest = $ Response area.
Sam will make at least $500 in interest.
606.74139.08141.17
Answers
GPT-4o mini
To determine how much Sam will earn each quarter and whether he will make at least $500 in interest, we can follow these calculations:
1. **Calculate quarterly interest rate:**
- Annual interest rate = 6%
- Quarterly interest rate = 6% / 4 = 1.5% = 0.015 (in decimal)
2. **Calculate interest for each quarter:**
- Amount deposited = $9,000
- Interest for each quarter:
- **First quarter:**
\[
\text{First quarter interest} = 9000 \times 0.015 = 135
\]
- **Second quarter:**
\[
\text{Balance after first quarter} = 9000 + 135 = 9135
\]
\[
\text{Second quarter interest} = 9135 \times 0.015 = 137.025
\]
- **Third quarter:**
\[
\text{Balance after second quarter} = 9135 + 137.025 = 9272.025
\]
\[
\text{Third quarter interest} = 9272.025 \times 0.015 = 139.080375
\]
- **Fourth quarter:**
\[
\text{Balance after third quarter} = 9272.025 + 139.080375 = 9411.105375
\]
\[
\text{Fourth quarter interest} = 9411.105375 \times 0.015 = 141.166585625
\]
3. **Total interest earned at the end of the year:**
- Total interest = First quarter interest + Second quarter interest + Third quarter interest + Fourth quarter interest
- Total interest = 135 + 137.025 + 139.080375 + 141.166585625
- Total interest ≈ 135 + 137.025 + 139.08 + 141.17 ≈ 552.275375
Based on these calculations:
- **Second quarter interest:** $137.025
- **Third quarter interest:** $139.08
- **Fourth quarter interest:** $141.17
- Sam will make at least $500 in interest since his total interest earned is approximately $552.28.
Now, let's place the correct values in the response areas provided:
- First quarter interest = $135.
- Second quarter interest = $137.03 (rounding to two decimal places).
- Third quarter interest = $139.08 (already rounded).
- Fourth quarter interest = $141.17 (already rounded).
Given that the amounts can be inserted:
- **First quarter interest =** $135.
- **Second quarter interest =** $137.03.
- **Third quarter interest =** $139.08.
- **Fourth quarter interest =** $141.17.
Sam will indeed make at least $500 in interest based on these calculations.
1. **Calculate quarterly interest rate:**
- Annual interest rate = 6%
- Quarterly interest rate = 6% / 4 = 1.5% = 0.015 (in decimal)
2. **Calculate interest for each quarter:**
- Amount deposited = $9,000
- Interest for each quarter:
- **First quarter:**
\[
\text{First quarter interest} = 9000 \times 0.015 = 135
\]
- **Second quarter:**
\[
\text{Balance after first quarter} = 9000 + 135 = 9135
\]
\[
\text{Second quarter interest} = 9135 \times 0.015 = 137.025
\]
- **Third quarter:**
\[
\text{Balance after second quarter} = 9135 + 137.025 = 9272.025
\]
\[
\text{Third quarter interest} = 9272.025 \times 0.015 = 139.080375
\]
- **Fourth quarter:**
\[
\text{Balance after third quarter} = 9272.025 + 139.080375 = 9411.105375
\]
\[
\text{Fourth quarter interest} = 9411.105375 \times 0.015 = 141.166585625
\]
3. **Total interest earned at the end of the year:**
- Total interest = First quarter interest + Second quarter interest + Third quarter interest + Fourth quarter interest
- Total interest = 135 + 137.025 + 139.080375 + 141.166585625
- Total interest ≈ 135 + 137.025 + 139.08 + 141.17 ≈ 552.275375
Based on these calculations:
- **Second quarter interest:** $137.025
- **Third quarter interest:** $139.08
- **Fourth quarter interest:** $141.17
- Sam will make at least $500 in interest since his total interest earned is approximately $552.28.
Now, let's place the correct values in the response areas provided:
- First quarter interest = $135.
- Second quarter interest = $137.03 (rounding to two decimal places).
- Third quarter interest = $139.08 (already rounded).
- Fourth quarter interest = $141.17 (already rounded).
Given that the amounts can be inserted:
- **First quarter interest =** $135.
- **Second quarter interest =** $137.03.
- **Third quarter interest =** $139.08.
- **Fourth quarter interest =** $141.17.
Sam will indeed make at least $500 in interest based on these calculations.