Math Problem Statement
Charlotte invested $730 in an account paying an interest rate of 3, one half3 2 1 % compounded continuously. Khalil invested $730 in an account paying an interest rate of 3, start fraction, 7, divided by, 8, end fraction3 8 7 % compounded daily. After 8 years, how much more money would Khalil have in his account than Charlotte, to the nearest dollar?
Solution
To solve this problem, we will calculate the amount of money in Charlotte's and Khalil's accounts after 8 years, using the respective interest rates and compounding methods.
Charlotte's Account:
- Principal:
- Interest rate: (since 3% = 3.5%)
- Time: years
- Compounding: Continuously
For continuous compounding, the formula is: Where:
- is the principal
- is the interest rate (in decimal)
- is the time in years
- is Euler's number (approximately 2.71828)
Plugging in the values for Charlotte:
Khalil's Account:
- Principal:
- Interest rate: (since % = 0.875%)
- Time: years
- Compounding: Daily (365 times a year)
For daily compounding, the formula is: Where:
- is the principal
- is the interest rate (in decimal)
- is the time in years
- is the number of times the interest is compounded per year
Plugging in the values for Khalil:
Now, let's calculate both amounts and find the difference.It seems like I can’t do more advanced data analysis right now. Please try again later.
If you'd like, I can walk you through the steps to calculate it manually. Let me know if you'd like assistance with that!
Here are 5 related questions you might find interesting:
- What are the differences between continuous and daily compounding interest methods?
- How does the interest rate affect compound growth over long periods of time?
- How can we use the compound interest formula for quarterly compounding?
- What is the significance of Euler's number in continuous compounding?
- How can the number of compounding periods per year impact overall returns?
Tip: When comparing two investments, small differences in interest rates or compounding frequency can lead to significant differences in returns over time.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Compound Interest
Continuous Compounding
Daily Compounding
Exponential Growth
Formulas
A = P * e^(rt) for continuous compounding
A = P * (1 + r/n)^(nt) for daily compounding
Theorems
Exponential Growth and Decay
Compound Interest Theorem
Suitable Grade Level
Grades 10-12
Related Recommendation
Comparing Investments: 7% Compounded Monthly vs. 6.8% Compounded Continuously for 6 Years
Investment Comparison: 7.22% Compounded Daily vs 7.3% Compounded Quarterly
Comparison of Continuous vs. Monthly Compounding for Investments
Compare Compound Interest for Different Interest Rates and Compounding Frequencies
Continuous vs Daily Compounded Interest Comparison