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The image you've uploaded contains a few compound interest problems. Let's focus on solving a couple of them.

### Formula for Compound Interest:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial sum of money).
- $ r $ is the annual interest rate (in decimal form, so 5% would be 0.05).
- $ t $ is the time the money is invested or borrowed for, in years.
- $ n $ is the number of times that interest is compounded per year.

### 7. Compounded Monthly, $ P = 2000 $, $ r = 3\% $, $ t = 5 $ years
This is a monthly compounded interest problem with:
- $ P = 2000 $
- $ r = 3\% = 0.03 $
- $ t = 5 $
- $ n = 12 $ (monthly compounding)

Substitute these values into the formula:
\[
A = 2000 \left(1 + \frac{0.03}{12}\right)^{12 \times 5}
\]

### 8. Compounded Monthly, $ P = 1500 $, $ r = 1.5\% $, $ t = 6 $ years
For this, we have:
- $ P = 1500 $
- $ r = 1.5\% = 0.015 $
- $ t = 6 $
- $ n = 12 $ (monthly compounding)

Substitute these values into the formula:
\[
A = 1500 \left(1 + \frac{0.015}{12}\right)^{12 \times 6}
\]

### 12. Compounded Daily, $ P = 1500 $, $ r = 4.5\% $, $ t = 3 $ years
In this case:
- $ P = 1500 $
- $ r = 4.5\% = 0.045 $
- $ t = 3 $
- $ n = 365 $ (daily compounding)

Substitute these values into the formula:
\[
A = 1500 \left(1 + \frac{0.045}{365}\right)^{365 \times 3}
\]

I can calculate these values for you, or would you prefer to go through any specific problem in detail? Let me know!

Find the total amount of money in an account at the end of the given time period. For example, compounded monthly with P = $2,000, r = 3%, t = 5 years.

Learn how to calculate compound interest for an initial principal of $2,000 at an annual interest rate of 3%, compounded monthly over 5 years. This example covers essential concepts in exponential growth and the compound interest formula.

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