An initial investment of $1000 is appreciated for 4 years in an account that earns 6% interest, 2)

compounded semiannually. Find the amount of money in the account at the end of the period.

What is 1000(1.03)^8 ?

1,266

To find the amount of money in the account at the end of the 4-year period, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A: The future value of the investment
P: The initial investment amount ($1000)
r: The interest rate (6% or 0.06 as a decimal)
n: The number of times interest is compounded per year (2, since it's compounded semiannually)
t: The number of years (4)

Plugging in the values into the formula, we get:

A = 1000(1 + 0.06/2)^(2 * 4)

Let's solve this equation step by step:

1. Calculate the value inside the parentheses:
0.06/2 = 0.03

2. Calculate the exponent:
2 * 4 = 8

3. Calculate the value inside the parentheses plus 1:
1 + 0.03 = 1.03

4. Raise this value to the power of 8:
1.03^8 ≈ 1.265317

5. Multiply the initial investment by this value:
1000 * 1.265317 ≈ 1265.32

Therefore, at the end of the 4-year period, the amount of money in the account will be approximately $1265.32.