Question
Three friends decide that they each want to be able to buy a new bike in four years.
Iliana puts $500 in a savings account with a simple interest rate of 4%.
Joann invests $515 in a standard savers account with a simple interest rate of 3%.
Cyndy invests $500 in a junior achievers account with a 3.5% compound interest rate.
Using the formula I = P r t for simple interest and A = P (1 + r) Superscript t for compound interest, who will have the most money to spend on a new bike at the end of the four years?
Joann will have the most money, $576.80 for the bike
Cyndy will have the most money, $580.00 for the bike.
Cyndy will have $576.80, the most money for the bike.
Iliana will have $580.00, the most money for the bike.
Iliana puts $500 in a savings account with a simple interest rate of 4%.
Joann invests $515 in a standard savers account with a simple interest rate of 3%.
Cyndy invests $500 in a junior achievers account with a 3.5% compound interest rate.
Using the formula I = P r t for simple interest and A = P (1 + r) Superscript t for compound interest, who will have the most money to spend on a new bike at the end of the four years?
Joann will have the most money, $576.80 for the bike
Cyndy will have the most money, $580.00 for the bike.
Cyndy will have $576.80, the most money for the bike.
Iliana will have $580.00, the most money for the bike.
Answers
GPT-4o mini
To find out who will have the most money at the end of four years, let's calculate the final amounts for each friend using the corresponding formulas for simple and compound interest.
**Iliana's Investment:**
- Principal (P) = $500
- Rate (r) = 4% = 0.04
- Time (t) = 4 years
Using the simple interest formula \( I = P \cdot r \cdot t \):
\[ I = 500 \cdot 0.04 \cdot 4 = 500 \cdot 0.16 = 80 \]
Total amount (A) = Principal + Interest = \( 500 + 80 = 580 \)
**Joann's Investment:**
- Principal (P) = $515
- Rate (r) = 3% = 0.03
- Time (t) = 4 years
Using the simple interest formula \( I = P \cdot r \cdot t \):
\[ I = 515 \cdot 0.03 \cdot 4 = 515 \cdot 0.12 = 61.80 \]
Total amount (A) = Principal + Interest = \( 515 + 61.80 = 576.80 \)
**Cyndy's Investment:**
- Principal (P) = $500
- Rate (r) = 3.5% = 0.035
- Time (t) = 4 years
Using the compound interest formula \( A = P (1 + r)^t \):
\[ A = 500 \cdot (1 + 0.035)^4 \]
\[ A = 500 \cdot (1.035)^4 \]
Calculating \( (1.035)^4 \):
\[ (1.035)^4 \approx 1.148882 \]
Thus,
\[ A = 500 \cdot 1.148882 \approx 574.441 \]
Now we can summarize the amounts:
- Iliana: $580.00
- Joann: $576.80
- Cyndy: $574.44 (approximately)
Thus, the final amounts are as follows:
- Iliana will have $580.00.
- Joann will have $576.80.
- Cyndy will have approximately $574.44.
**Conclusion:**
Iliana will have the most money to spend on a new bike at the end of the four years: **Iliana will have $580.00, the most money for the bike.**
**Iliana's Investment:**
- Principal (P) = $500
- Rate (r) = 4% = 0.04
- Time (t) = 4 years
Using the simple interest formula \( I = P \cdot r \cdot t \):
\[ I = 500 \cdot 0.04 \cdot 4 = 500 \cdot 0.16 = 80 \]
Total amount (A) = Principal + Interest = \( 500 + 80 = 580 \)
**Joann's Investment:**
- Principal (P) = $515
- Rate (r) = 3% = 0.03
- Time (t) = 4 years
Using the simple interest formula \( I = P \cdot r \cdot t \):
\[ I = 515 \cdot 0.03 \cdot 4 = 515 \cdot 0.12 = 61.80 \]
Total amount (A) = Principal + Interest = \( 515 + 61.80 = 576.80 \)
**Cyndy's Investment:**
- Principal (P) = $500
- Rate (r) = 3.5% = 0.035
- Time (t) = 4 years
Using the compound interest formula \( A = P (1 + r)^t \):
\[ A = 500 \cdot (1 + 0.035)^4 \]
\[ A = 500 \cdot (1.035)^4 \]
Calculating \( (1.035)^4 \):
\[ (1.035)^4 \approx 1.148882 \]
Thus,
\[ A = 500 \cdot 1.148882 \approx 574.441 \]
Now we can summarize the amounts:
- Iliana: $580.00
- Joann: $576.80
- Cyndy: $574.44 (approximately)
Thus, the final amounts are as follows:
- Iliana will have $580.00.
- Joann will have $576.80.
- Cyndy will have approximately $574.44.
**Conclusion:**
Iliana will have the most money to spend on a new bike at the end of the four years: **Iliana will have $580.00, the most money for the bike.**