Find the amount that schould be invested now to accumulate following amounts,if te money is compounded as indicated.
$2000 at 9% compund semiannually for 8 years. i don't know how u do this
sorry, your homework!!!!!!!!!!!!!!!!!!
Double post. I answered this below.
To calculate the amount that should be invested now to accumulate a specific amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, we need to find the principal amount (P), so we rearrange the formula:
P = A / (1 + r/n)^(nt)
Given the following values:
A = $2000
r = 9% = 0.09 (expressed as a decimal)
n = 2 (compounded semiannually)
t = 8 years
Now we can substitute these values into the formula and calculate the principal amount:
P = 2000 / (1 + 0.09/2)^(2*8)
First, let's simplify the equation inside the parentheses:
P = 2000 / (1 + 0.045)^(16)
Next, evaluate the expression inside the parentheses:
P = 2000 / (1.045)^(16)
Now raise 1.045 to the power of 16:
P = 2000 / 1.836723
Finally, divide $2000 by 1.836723 to find the principal amount:
P ≈ $1089.02
Therefore, approximately $1089.02 should be invested now to accumulate $2000 after 8 years with a compound interest rate of 9% compounded semiannually.