16000((1+.05/2)^3 - 1 - .05*3/2) = 30.25
Now, if you meant 3 1/2 years, fix it up.
Now, if you meant 3 1/2 years, fix it up.
First, let's calculate the simple interest using the formula: Simple Interest = (Principal * Rate * Time) / 100.
Principal = $16,000
Rate = 5% per annum
Time = 3/2 years = 1.5 years
Simple Interest = (16000 * 5 * 1.5) / 100 = $1,200
Now, let's calculate the compound interest, which is compounded half-yearly. The formula for compound interest is:
Compound Interest = Principal * (1 + Rate / n)^(n * Time) - Principal
Where n represents the number of compounding periods per year.
Given that the compound interest is reckoned half-yearly, the number of compounding periods per year (n) = 2.
Compound Interest = 16000 * (1 + 0.05 / 2)^(2 * 1.5) - 16000
Compound Interest = 16000 * (1.025)^3 - 16000
Compound Interest ≈ $1,241.35
Now we can calculate the difference between the simple interest and compound interest.
Difference = Compound Interest - Simple Interest
Difference = $1,241.35 - $1,200
Difference ≈ $41.35
Therefore, the difference between the simple interest and compound interest on $16,000 for 3/2 years at 5% per annum, compounded half-yearly, is approximately $41.35.
First, let's calculate the simple interest.
Simple Interest (SI) = (Principal * Rate * Time) / 100
Where:
Principal = 16000
Rate = 5%
Time = 3/2 years
SI = (16000 * 5 * (3/2)) / 100
SI = 1200
Now, let's calculate the compound interest. Since the interest is compounded semi-annually, we will need to split the time period into two halves (6 months each).
Compound Interest (CI) = P * [(1 + r/n)^(n*t) - 1]
Where:
P = Principal
r = Rate / 100
n = Number of compounding periods per year
t = Total number of years
Principal = 16000
Rate = 5%
Time = 3/2 years (or 1.5 years)
Compounding periods per year = 2 (since interest is compounded half-yearly)
CI = 16000 * [(1 + 0.05/2)^(2*1.5) - 1]
CI = 16000 * (1.025)^3 - 1
CI ≈ 16000 * 1.0770388 - 1
CI ≈ 17232.62 - 1
CI ≈ 17231.62
Now, let's find the difference between the compound interest and simple interest.
Difference = Compound Interest - Simple Interest
Difference = CI - SI
Difference = 17231.62 - 1200
Difference ≈ 16031.62
Therefore, the difference between the simple interest and compound interest on 16000 for 3/2 years at 5% per annum (compounded semi-annually) is approximately 16031.62.