Find the accumulated amount after 7 years if $17,000 is invested at 4.5%/year compounded in the following ways. (Round your answers to the nearest cent.)
(a) compounded annually
$   

 

(b) compounded semiannually
$   

 

(c) compounded quarterly
$   

 

(d) compounded monthly
$   


The formula for compound interest is given by:

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

Where:
- $ A $ is the accumulated amount (future value)
- $ P $ is the principal (initial investment)
- $ r $ is the annual interest rate (in decimal form)
- $ n $ is the number of times interest is compounded per year
- $ t $ is the time the money is invested for (in years)

Given:
- $ P = 17,000 $
- $ r = 4.5\% = 0.045 $
- $ t = 7 $ years

Now let's solve for each case:

### (a) Compounded annually ($n = 1$):
\[
A = 17,000 \left(1 + \frac{0.045}{1}\right)^{1 \times 7}
\]

### (b) Compounded semiannually ($n = 2$):
\[
A = 17,000 \left(1 + \frac{0.045}{2}\right)^{2 \times 7}
\]

### (c) Compounded quarterly ($n = 4$):
\[
A = 17,000 \left(1 + \frac{0.045}{4}\right)^{4 \times 7}
\]

### (d) Compounded monthly ($n = 12$):
\[
A = 17,000 \left(1 + \frac{0.045}{12}\right)^{12 \times 7}
\]

Let me calculate each of these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to continue solving this step manually, or perhaps revisit it later? Let me know if you'd like help with any part of the process.

Here are 5 related questions to explore:
1. What is the difference between simple interest and compound interest?
2. How does increasing the frequency of compounding affect the accumulated amount?
3. Can compound interest be negative, and under what conditions?
4. What is continuous compounding, and how does it differ from regular compounding?
5. How does the principal amount influence the growth of an investment over time?

**Tip:** In financial calculations, even small changes in the interest rate or compounding frequency can have significant effects over long periods of time.

Find the accumulated amount after 7 years if $17,000 is invested at 4.5%/year compounded in the following ways. (Round your answers to the nearest cent.) (a) compounded annually (b) compounded semiannually (c) compounded quarterly (d) compounded monthly

Learn how to calculate the accumulated amount after investing $17,000 at an annual interest rate of 4.5% over 7 years, compounded annually, semiannually, quarterly, and monthly. This problem uses the compound interest formula, ideal for students in Grades 10-12.

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