If 47100 dollars is invested at an interest rate of 6 percent per year, compounded semiannually, find the value of the investment after the given number of years. Round value to the nearest cent.


(a) 5 years:
Your answer is 

(b) 10 years:
Your answer is 

(c) 15 years:
Your answer is 



The formula for compound interest is given by:

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

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

In this case:
- $P = 47100$
- $r = 0.06$ (6% annual interest)
- $n = 2$ (compounded semiannually)
- $t = 5, 10, 15$ for each case.

Let's calculate the future value of the investment for each time period.

### (a) After 5 years:
\[
A = 47100 \left(1 + \frac{0.06}{2}\right)^{2 \times 5}
\]
\[
A = 47100 \left(1 + 0.03\right)^{10}
\]
\[
A = 47100 \times (1.03)^{10}
\]

Let me calculate that.

### (b) After 10 years:
\[
A = 47100 \left(1 + \frac{0.06}{2}\right)^{2 \times 10}
\]
\[
A = 47100 \times (1.03)^{20}
\]

### (c) After 15 years:
\[
A = 47100 \left(1 + \frac{0.06}{2}\right)^{2 \times 15}
\]
\[
A = 47100 \times (1.03)^{30}
\]

Let me calculate all these values for you.The value of the investment after the given number of years is as follows:

(a) After 5 years: \$63,298.46

(b) After 10 years: \$85,067.84

(c) After 15 years: \$114,324.06

Let me know if you need further clarification or details on these calculations.

Here are some related questions you might find useful:
1. What would happen if the interest was compounded quarterly instead?
2. How does the investment grow with continuous compounding?
3. How much would the investment be worth if withdrawn after 8 years?
4. What is the total interest earned after 15 years?
5. How would the results change with a different interest rate (e.g., 4%)?

**Tip**: The more frequently interest is compounded, the faster the investment grows!

If 47100 dollars is invested at an interest rate of 6 percent per year, compounded semiannually, find the value of the investment after the given number of years. Round value to the nearest cent.
(a) 5 years
(b) 10 years
(c) 15 years

Learn how to calculate compound interest on an investment of $47,100 at a 6% annual interest rate, compounded semiannually, over 5, 10, and 15 years. This guide provides a step-by-step solution to find the investment value after each period using the compound interest formula.

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