An amount of $6,010 is deposited into an account earning 8% interest compounded quarterly. How much will be in the account in 8 years and 3 months? Round the answer to the *nearest cent*.   I/Y =

To determine the amount in the account after 8 years and 3 months with quarterly compounding, we can use the compound interest formula:

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

where:
- $ A $ is the future value of the investment.
- $ P = 6,010 $ is the initial principal.
- $ r = 0.08 $ is the annual interest rate (8%).
- $ n = 4 $ is the number of times interest is compounded per year (quarterly).
- $ t = 8.25 $ years (since 3 months is 0.25 years).

Let's solve step-by-step:

### Step 1: Substitute values into the formula
\[
A = 6,010 \left(1 + \frac{0.08}{4}\right)^{4 \cdot 8.25}
\]

### Step 2: Simplify the terms
1. Calculate the quarterly interest rate: $\frac{0.08}{4} = 0.02$.
2. Calculate the number of compounding periods over 8.25 years: $4 \times 8.25 = 33$.

### Step 3: Calculate $A$
\[
A = 6,010 \left(1 + 0.02\right)^{33}
\]
\[
A = 6,010 \times (1.02)^{33}
\]

### Step 4: Compute $(1.02)^{33}$
\[
(1.02)^{33} \approx 1.9057
\]

### Step 5: Multiply by the principal
\[
A \approx 6,010 \times 1.9057 \approx 11,452.24
\]

### Final Answer
The amount in the account after 8 years and 3 months is **$11,452.24** (rounded to the nearest cent).

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**I/Y (Interest per period)**

Since interest is compounded quarterly, we divide the annual rate by 4:

\[
I/Y = \frac{0.08}{4} = 0.02 \text{ or } 2\%
\]

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Would you like more details or have questions?

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1. How would the amount change if compounded monthly?
2. How does the amount vary if the interest rate changes?
3. What is the effect of a longer time period?
4. How does compounding frequency impact final value?
5. How is quarterly compounding different from annual compounding?

**Tip:** When dealing with compound interest, increase compounding frequency for faster growth!

An amount of $6,010 is deposited into an account earning 8% interest compounded quarterly. How much will be in the account in 8 years and 3 months? Round the answer to the nearest cent.

Find out how much an initial deposit of $6,010 grows in an account with 8% interest compounded quarterly over 8 years and 3 months. This guide includes step-by-step calculations using the compound interest formula, covering essential concepts for high school students (Grades 10-12).

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