Find the accumulated amount after 7 years if $11,000 is invested at 5%/year compounded in the following ways. (Round your answers to the nearest cent.) Compounded annually, semiannually, quarterly, and monthly


To calculate the accumulated amount for different compounding frequencies, we use the formula for compound interest:

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

Where:
- $ A $ is the accumulated amount
- $ P $ is the principal amount ($11,000)
- $ r $ is the annual interest rate (5% or 0.05)
- $ n $ is the number of times interest is compounded per year
- $ t $ is the number of years (7 years)

### 1. Compounded Annually ($n = 1$):
\[
A = 11,000 \left(1 + \frac{0.05}{1}\right)^{1 \times 7}
\]
\[
A = 11,000 \times (1.05)^7
\]

### 2. Compounded Semiannually ($n = 2$):
\[
A = 11,000 \left(1 + \frac{0.05}{2}\right)^{2 \times 7}
\]
\[
A = 11,000 \times \left(1 + 0.025\right)^{14}
\]

### 3. Compounded Quarterly ($n = 4$):
\[
A = 11,000 \left(1 + \frac{0.05}{4}\right)^{4 \times 7}
\]
\[
A = 11,000 \times \left(1 + 0.0125\right)^{28}
\]

### 4. Compounded Monthly ($n = 12$):
\[
A = 11,000 \left(1 + \frac{0.05}{12}\right)^{12 \times 7}
\]
\[
A = 11,000 \times \left(1 + 0.0041667\right)^{84}
\]

Let me calculate these values for you.The accumulated amounts after 7 years for $11,000 invested at 5% annual interest, compounded in different ways, are as follows:

1. **Compounded annually:** $15,478.10
2. **Compounded semiannually:** $15,542.71
3. **Compounded quarterly:** $15,575.92
4. **Compounded monthly:** $15,598.40

Would you like a detailed explanation of any part of this process or have further questions?

Here are five related questions:
1. What would the accumulated amount be if compounded daily?
2. How does increasing the compounding frequency affect the accumulated amount?
3. What is the formula for continuous compounding?
4. How would the accumulated amount change if the interest rate increased to 6%?
5. How does the accumulated amount differ if the investment is only for 5 years?

**Tip:** More frequent compounding results in a slightly higher accumulated amount because interest is applied more often during the year.

Find the accumulated amount after 7 years if $11,000 is invested at 5%/year compounded in the following ways. (Round your answers to the nearest cent.) Compounded annually, semiannually, quarterly, and monthly.

Learn how to calculate the accumulated amount for $11,000 invested at a 5% annual interest rate, compounded annually, semiannually, quarterly, and monthly over 7 years. This detailed solution covers the use of the compound interest formula and demonstrates the effects of varying compounding frequencies. Suitable for students in Grades 9-12.

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