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.