find the accumulated value of an investment of $2000 at 8% compounded semiannually for 9 years.
Use formula A=P[1+(r)(n)^nt
hmm, what else would I use?
r = .04 per half year
n = 18 half years
so
A = 2000 [1.04^18] = 2000*2.02 = $4051.63
we more than doubled our money - good move.
To find the accumulated value of an investment, we can use the formula A = P[1 + (r/n)^(nt)], where:
A = accumulated value
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $2000
r = 8% (or 0.08 as a decimal)
n = 2 (compounded semiannually)
t = 9 years
Substituting these values into the formula:
A = 2000 * [1 + (0.08/2)^(2*9)]
Now, let's calculate the accumulated value:
A = 2000 * [1 + 0.04]^(18)
A = 2000 * (1.04)^(18)
A ≈ 2000 * 2.091623
A ≈ $4183.25
Therefore, the accumulated value of the investment of $2000 at 8% compounded semiannually for 9 years is approximately $4183.25.