Find the accumulated value of an investment of $15,000 at 7% compounded semiannually for 4 yrs
V = Po(1+r)^n.
r = (7% / 2) / 100% = 0.035 = Semi-annual % rate expressed as a decimal.
n = 2 comp./yr * 4yrs = 8 Compounding
periods.
V = $15,000(1.035)^8 = $19,752.14.
To calculate the accumulated value of an investment with compound interest, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated value
P = Principal amount (initial investment)
r = Annual interest rate
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $15,000, the annual interest rate (r) is 7%, the number of times interest is compounded per year (n) is 2 (semiannually), and the number of years (t) is 4.
Plugging in these values into the formula:
A = 15000(1 + 0.07/2)^(2 * 4)
A = 15000(1 + 0.035)^(8)
A = 15000(1.035)^(8)
Using a calculator or performing the calculations step by step:
A = 15000 * 1.3196753
A ≈ $19,795.13
Therefore, the accumulated value of the investment after 4 years will be approximately $19,795.13.
To find the accumulated value of an investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated value after time t
P = 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, we have:
P = $15,000
r = 7% or 0.07 (decimal form)
n = 2 (compounded semiannually, so twice a year)
t = 4 years
Now, let's substitute these values into the formula and calculate:
A = 15000(1 + 0.07/2)^(2*4)
A = 15000(1 + 0.035)^(8)
A = 15000(1.035)^(8)
A ≈ 15000(1.326)
A ≈ $19,890
Therefore, the accumulated value of the investment after 4 years would be approximately $19,890.