To calculate the future value of an investment compounded semiannually, we can use the future value formula: FV = P(1 + r/n)^(nt), where:
- FV = future value
- P = principal amount (the initial investment)
- r = annual interest rate (decimal)
- n = number of times interest is compounded per year
- t = number of years the money is invested or borrowed
In this case, we have:
- P = $1000
- r = 8% = 0.08
- n = 2 (since it is compounded semiannually)
- t = 5 years
Using the formula, we insert the values:
FV = 1000(1 + 0.08/2)^(2*5)
Now let’s break this down step by step:
- Calculate the interest rate per compounding period: 0.08/2 = 0.04.
- Calculate the total number of compounding periods: 2*5 = 10.
- Calculate the expression inside the parentheses: 1 + 0.04 = 1.04.
- Raise it to the power of the total number of compounding periods: (1.04)^10 ≈ 1.48024.
- Finally, multiply by the principal: FV ≈ 1000 * 1.48024 ≈ 1480.24.
Therefore, the future value of a $1000 investment today at an 8 percent annual interest rate compounded semiannually for 5 years is approximately $1480.24.