Person A deposits 

​$27002700 

in an account that pays 

55​% 

interest compounded once a year.  Person B deposits 

​$23502350 

in an account that pays 

66​% 

interest compounded monthly.

To compare the two deposits, we need to calculate the future value (FV) of both Person A's and Person B's investments, considering the different interest rates and compounding frequencies.

### Formula for Compound Interest:
The general formula for compound interest is:

\[
FV = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ FV $ = Future value of the investment/loan
- $ P $ = Principal amount (initial investment)
- $ r $ = Annual interest rate (in decimal form, e.g., 5% = 0.05)
- $ n $ = Number of times the interest is compounded per year
- $ t $ = Time the money is invested for, in years

### Person A's Investment
- Principal $ P = 2700 $
- Interest rate $ r = 5\% = 0.05 $
- Compounding frequency $ n = 1 $ (once a year)

The future value after $ t $ years for Person A is:

\[
FV_A = 2700 \left(1 + \frac{0.05}{1}\right)^{1t} = 2700 (1.05)^t
\]

### Person B's Investment
- Principal $ P = 2350 $
- Interest rate $ r = 6\% = 0.06 $
- Compounding frequency $ n = 12 $ (monthly)

The future value after $ t $ years for Person B is:

\[
FV_B = 2350 \left(1 + \frac{0.06}{12}\right)^{12t} = 2350 \left(1 + 0.005\right)^{12t} = 2350 (1.005)^{12t}
\]

Both future values will depend on the number of years $ t $ the money is invested for. Let me know if you'd like to calculate the future values for specific $ t $ values, or if you'd like a comparison between the two investments for different time periods!

Would you like to calculate for a specific time period, or do you have any questions?

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Here are 5 related questions to explore further:
1. What is the future value of Person A's investment after 5 years?
2. How does the compounding frequency affect the total interest earned in Person B's account?
3. What is the total interest earned by both persons after 10 years?
4. How would the future value change if Person B's interest rate was compounded annually instead of monthly?
5. What happens to the future value if Person A increases their deposit amount?

**Tip:** The more frequently interest is compounded, the more interest is earned over time due to the effect of "interest on interest."

Person A deposits $2700 in an account that pays 5% interest compounded once a year. Person B deposits $2350 in an account that pays 6% interest compounded monthly. What will the future value of both investments be after a specific time period?

Learn how to compare two investments: Person A with $2700 at 5% interest compounded annually, and Person B with $2350 at 6% interest compounded monthly. Explore the compound interest formula and understand how compounding frequency affects future value over time. Suitable for Grades 10-12 students.

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