Find to the nearest dollar, the compound interest on $50,000 at 8% p.a. for 5 years.

To find the compound interest on $50,000 at an annual interest rate of 8% for 5 years, we use the compound interest formula:

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

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 (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for in years.

For this problem:
- $ P = 50,000 $
- $ r = 0.08 $
- $ n = 1 $ (compounded annually)
- $ t = 5 $

Plug these values into the formula:

\[ A = 50,000 \left(1 + \frac{0.08}{1}\right)^{1 \times 5} \]
\[ A = 50,000 \left(1 + 0.08\right)^5 \]
\[ A = 50,000 (1.08)^5 \]

Now, calculate $ (1.08)^5 $:

\[ (1.08)^5 \approx 1.4693 \]

Then multiply by the principal amount:

\[ A \approx 50,000 \times 1.4693 \]
\[ A \approx 73,465 \]

The amount of money accumulated after 5 years is approximately $73,465. 

To find the compound interest, subtract the principal from this amount:

\[ \text{Compound Interest} = A - P \]
\[ \text{Compound Interest} = 73,465 - 50,000 \]
\[ \text{Compound Interest} \approx 23,465 \]

So, the compound interest on $50,000 at 8% per annum for 5 years is approximately $23,465.

Would you like details or have any questions? Here are some related questions to explore further:

1. How would the interest change if compounded semi-annually?
2. What if the interest rate was 6% instead of 8%?
3. How does the compound interest formula differ from the simple interest formula?
4. How much would the compound interest be for a period of 10 years instead of 5?
5. What is the effective annual rate (EAR) for an 8% nominal rate compounded annually?
6. How would you calculate the compound interest if it was compounded monthly?
7. What happens to the compound interest if the principal amount is doubled?
8. How would the final amount change if the interest rate is compounded daily?

**Tip:** When dealing with compound interest, always check the compounding frequency (annually, semi-annually, quarterly, etc.) as it significantly affects the final amount.

Learn how to calculate compound interest on $50,000 at an 8% annual interest rate over a period of 5 years. Understand the compound interest formula and step-by-step calculation process. Approximate the compound interest to the nearest dollar.

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