Find the future value of $600 invested for 5 years at 8% interest compounded semiannually.
What is 600(1.04)^10 ?
dsgerhretshraegre
To find the future value of an investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $600
r = 8% = 0.08 (since it needs to be in decimal form)
n = 2 (compounded semiannually)
t = 5 years
Plugging these values into the formula, we have:
A = 600(1 + 0.08/2)^(2*5)
Let's calculate this step by step:
Step 1: Divide the annual interest rate by the number of times compounded per year:
0.08/2 = 0.04
Step 2: Multiply the number of times compounded per year by the number of years:
2 * 5 = 10
Now, let's continue with the calculation:
A = 600(1 + 0.04)^10
A = 600(1.04)^10
Calculating the values within parentheses first:
1.04^10 ≈ 1.48886
A = 600(1.48886)
A ≈ $893.32
Therefore, the future value of $600 invested for 5 years at 8% interest compounded semiannually is approximately $893.32.