Math Problem Statement
Complete the table and find the balance A if
$45004500
is invested at an annual percentage rate of
33%
for 10 years and compounded n times a year.
Solution
To complete the table and find the balance , we use the compound interest formula:
Where:
- is the principal amount ($4500)
- is the annual interest rate (33% or 0.33)
- is the number of times interest is compounded per year
- is the time in years (10 years)
- is the amount after time
Let's calculate for different values of :
1. (Compounded Annually):
2. (Compounded Quarterly):
3. (Compounded Monthly):
4. (Compounded Daily):
Now, let's compute these values.
I'll proceed to calculate these balances.Here are the balances for the different compounding frequencies:
- Compounded Annually ():
- Compounded Quarterly ():
- Compounded Monthly ():
- Compounded Daily ():
These values demonstrate how the frequency of compounding affects the final balance over time.
Do you want more details or have any questions?
Here are five related questions to consider:
- How would the balance change if the interest rate was lower?
- What happens to the balance if the investment period is reduced to 5 years?
- How does continuous compounding compare to daily compounding?
- What is the effect of doubling the initial investment amount?
- How would a semi-annual compounding frequency compare to the others?
Tip: The more frequently interest is compounded, the higher the final balance will be.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Exponential Growth
Formulas
Compound Interest Formula: A = P (1 + r/n)^(nt)
Theorems
-
Suitable Grade Level
High School
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