What's the accummulated full amount for a principal of $15,000 for 3 years at 4% compounded semi annually?
What is 15000(1.02)^6 ?
To calculate the accumulated full amount for a principal of $15,000 over 3 years at a 4% interest rate compounded semi-annually, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated full amount (including principal)
P = Principal amount ($15,000)
r = Annual interest rate (4% in decimal form, which is 0.04)
n = Number of times the interest is compounded per year (semi-annually means 2 times a year)
t = Number of years (3 years)
Now we can substitute the given values into the formula and calculate the result step by step:
1. Calculate the interest rate per compounding period:
r/n = 0.04 / 2 = 0.02
2. Calculate the total number of compounding periods:
nt = 3 * 2 = 6
3. Calculate the accumulated amount:
A = $15,000 * (1 + 0.02)^(6)
A ≈ $15,000 * (1.02)^(6)
A ≈ $15,000 * 1.12550879
A ≈ $16,882.63
Therefore, the accumulated full amount for a principal of $15,000 over 3 years at a 4% interest rate compounded semi-annually would be approximately $16,882.63.