Henry invested $4,100 in an account paying an interest rate of 3 3/8% compounded quarterly. Brooklyn invested $4,100 in an account paying an interest rate of 2 3/4% compounded monthly. After 20 years, how much more money would Henry have in his account than Brooklyn, to the nearest dollar?

To solve this problem, we can use the compound interest formula:

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

Where:
- $ A $ is the amount of money after $ t $ years.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the number of years.

### Henry's Account:
- Principal $ P = 4,100 $
- Annual interest rate $ r = 3\frac{3}{8}\% = \frac{27}{8}\% = 0.03375 $
- Compounded quarterly, so $ n = 4 $
- Time $ t = 20 $ years

For Henry, the formula becomes:

\[
A_H = 4,100 \left(1 + \frac{0.03375}{4}\right)^{4 \times 20}
\]

### Brooklyn's Account:
- Principal $ P = 4,100 $
- Annual interest rate $ r = 2\frac{3}{4}\% = 0.0275 $
- Compounded monthly, so $ n = 12 $
- Time $ t = 20 $ years

For Brooklyn, the formula becomes:

\[
A_B = 4,100 \left(1 + \frac{0.0275}{12}\right)^{12 \times 20}
\]

Now, let's calculate both $ A_H $ and $ A_B $ and find the difference between them.After 20 years, Henry's account will have approximately \$8,030, while Brooklyn's account will have approximately \$7,102. The difference between the two accounts is about \$928.

Would you like more details on any part of the calculation, or do you have any other questions?

Here are five related questions to explore:
1. How would the difference change if both accounts were compounded annually instead?
2. What if Brooklyn invested \$5,000 instead of \$4,100?
3. How would a higher interest rate (e.g., 5%) impact the final amounts?
4. What is the total interest earned by each person?
5. How long would it take for Henry's investment to double at his current rate?

**Tip:** Increasing the frequency of compounding results in slightly more interest, even with the same annual rate.

Discover how to compare the growth of two investments: Henry's $4,100 at 3 3/8% compounded quarterly and Brooklyn's $4,100 at 2 3/4% compounded monthly over 20 years. Learn how compound interest affects savings growth with step-by-step calculations.

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