what is the value of an account at the en of 4 years if $480 was origionally invested at a 10% interest rate compounded quarterly

To find the value of an account at the end of 4 years with an initial investment of $480 and a 10% annual interest rate compounded quarterly, we use the compound interest formula:

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

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

In this problem:
- $ P = 480 $
- $ r = 0.10 $
- $ n = 4 $ (since the interest is compounded quarterly)
- $ t = 4 $

Plugging these values into the formula, we get:

\[
A = 480 \left(1 + \frac{0.10}{4}\right)^{4 \times 4}
\]

Simplify the expression inside the parentheses:

\[
A = 480 \left(1 + 0.025\right)^{16}
\]

\[
A = 480 \left(1.025\right)^{16}
\]

Calculate $(1.025)^{16}$:

\[
(1.025)^{16} \approx 1.488864
\]

Now, multiply this by the principal:

\[
A \approx 480 \times 1.488864
\]

\[
A \approx 714.65
\]

Therefore, the value of the account at the end of 4 years is approximately \$714.65.

Would you like more details or have any questions?

Here are 8 related questions for further exploration:

1. How does the frequency of compounding affect the final amount?
2. What would be the final amount if the interest were compounded monthly instead?
3. How do you derive the compound interest formula?
4. What is the difference between compound interest and simple interest?
5. How would the final amount change if the interest rate were 8% instead of 10%?
6. How does continuous compounding differ from quarterly compounding?
7. Can you calculate the effective annual rate (EAR) given the quarterly compounding rate?
8. What real-world scenarios might require compound interest calculations?

**Tip:** When calculating compound interest, always ensure that the compounding period and the rate are aligned (e.g., if compounded quarterly, adjust the rate and number of periods accordingly).

Learn how to calculate the value of an account after 4 years with an initial investment of $480 at a 10% annual interest rate compounded quarterly. Step-by-step solution provided.

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