The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate.

Principal

Rate

Compounded

Time

$ 8000

5 %

semiannually

3 years

A.  Find how much money there will be in the account after the given number of years.

B.  Find the interest earned.

To solve this compound interest problem, we'll use the compound interest formula:

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

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

### Given Information:
- **Principal (P)** = $8000
- **Rate (r)** = 5% = 0.05
- **Compounded semiannually (n)** = 2
- **Time (t)** = 3 years

### A. Find how much money there will be in the account (A):

Using the formula, plug in the values:

\[
A = 8000 \left( 1 + \frac{0.05}{2} \right)^{2 \times 3}
\]

Now, let's calculate this.

\[
A = 8000 \left( 1 + 0.025 \right)^{6}
\]

\[
A = 8000 \left( 1.025 \right)^6
\]

Calculating further:

\[
A = 8000 \times 1.159694
\]

\[
A = 9277.55
\]

So, after 3 years, the amount in the account will be **$9277.55**.

### B. Find the interest earned:

The interest earned is the difference between the final amount $A$ and the initial principal $P$:

\[
\text{Interest} = A - P = 9277.55 - 8000 = 1277.55
\]

Thus, the interest earned over 3 years is **$1277.55**.

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Do you need any more details or clarifications?

### Related Questions:
1. What if the interest was compounded quarterly instead of semiannually?
2. How would the final amount change if the interest rate was increased to 6%?
3. What would the interest be if the deposit time was 5 years instead of 3 years?
4. How does continuous compounding affect the final amount?
5. How does simple interest compare to compound interest over the same period?

**Tip:** The more frequently interest is compounded, the more total interest will accumulate.

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Principal: $8000, Rate: 5%, Compounded semiannually, Time: 3 years. A. Find how much money there will be in the account after the given number of years. B. Find the interest earned.

Learn how to calculate the amount in a savings account after 3 years with an initial deposit of $8000 and a 5% interest rate compounded semiannually. This step-by-step guide includes the compound interest formula and explains how to find the interest earned. Suitable for high school students (Grades 9-12).

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