If ​$800 is invested at 8​% compounded 
​(A) annually,     ​ (B) quarterly,    ​ (C) monthly,
what is the amount after 5 ​years? How much interest is​ earned?
Question content area bottom
Part 1
​(A) If it is compounded​ annually, what is the​ amount? 
​$
  
enter your response here ​(Round to the nearest​ cent.)

The formula for compound interest is:

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

where:
- $ A $ is the future value of the investment/loan, including interest,
- $ P $ is the principal investment amount (initial deposit or loan),
- $ r $ is the annual interest rate (decimal),
- $ n $ is the number of times that interest is compounded per unit $ t $,
- $ t $ is the time the money is invested or borrowed for, in years.

Let's calculate part (A), where the interest is compounded annually.

- $ P = 800 $
- $ r = 0.08 $
- $ n = 1 $ (since it's compounded annually)
- $ t = 5 $

Now, we can plug the values into the formula:

\[
A = 800 \left( 1 + \frac{0.08}{1} \right)^{1 \times 5}
= 800 \left( 1.08 \right)^5
\]

Let me calculate that for you.The amount after 5 years, when compounded annually at 8%, is approximately **$1175.46**.

Now, to find the interest earned:

\[
\text{Interest} = A - P = 1175.46 - 800 = 375.46
\]

The interest earned is **$375.46**.

Would you like more details or have any other questions? Here are some related problems to consider:

1. How would the amount change if the interest rate was 10% instead of 8%?
2. What if the investment period was 10 years instead of 5 years?
3. How much would be earned if the interest was compounded daily?
4. What is the difference in the amount earned when compounded quarterly instead of annually?
5. Can you find the interest earned if the investment was only for 3 years?

**Tip:** Compounding frequency has a significant effect on the growth of an investment over time.

If $800 is invested at 8% compounded (A) annually, (B) quarterly, (C) monthly, what is the amount after 5 years? How much interest is earned? (A) If it is compounded annually, what is the amount? (Round to the nearest cent.)

Calculate the future value of $800 invested at 8% compounded annually, quarterly, and monthly over 5 years. Learn how to apply the compound interest formula to find the final amount and interest earned.

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