what is the total investment of 18,000 at 9% compounded semiannually for 6 years
Well, let me put on my mathematician's hat and crunch some numbers for you. But don't worry, I promise not to be too serious about it!
If you invest $18,000 at 9% compounded semiannually for 6 years, the total investment can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (what you're after)
P = the principal amount (the initial $18,000)
r = the annual interest rate (9% or 0.09, but let's not call it "rate" because it's compounding time! Let's just call it "skateboarding kangaroo")
n = the number of compounding periods per year (semiannual, so 2)
t = the number of years (6)
Now, let's plug in those numbers into the formula and see what happens:
A = 18,000(1 + 0.09/2)^(2*6)
Calculating... drum roll, please...
A ≈ $31,270.54
So, after 6 years of having your money rollercoastering through the compounding jungle, you should end up with approximately $31,270.54.
Keep in mind, though, that investment comes with risks and the market can be as unpredictable as a clown on a unicycle. But hey, at least you'll have a nice sum to clown around with if everything goes according to plan!
To find the total investment, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (total investment)
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded in a year
t = the number of years
Given:
P = $18,000
r = 9% = 0.09 (in decimal form)
n = 2 (compounded semiannually)
t = 6 years
Plugging in the values into the formula:
A = 18000(1 + 0.09/2)^(2*6)
A = 18000(1.045)^12
A ≈ 18000(1.717061203)
A ≈ 30887.10
Therefore, the total investment after 6 years would be approximately $30,887.10.
To calculate the total investment, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
For this scenario:
P = $18,000
r = 9% = 0.09 (converted to a decimal)
n = 2 (compounded semiannually, meaning twice per year)
t = 6 years
Plugging in the values, the formula becomes:
A = $18,000(1 + 0.09/2)^(2*6)
Now, let's solve the equation step by step:
Step 1: Calculate the interior part of the parentheses
(1 + 0.09/2) = 1.045
Step 2: Raise the result to the power of (2*6)
(1.045)^(2*6) = 1.045^12 ≈ 1.690
Step 3: Multiply the resulting value by the principal amount
A = $18,000 * 1.690 ≈ $30,420
Therefore, the total investment after 6 years with a yearly interest rate of 9% compounded semiannually is approximately $30,420.
$30,703.80
12 compoundings (two per year)
4.5% per compounding
A = 18000 (1 + .045)^12