Find the difference between the simple interest and compound interest on 16000 for 3/2 years at 5 %per annum, compound interest being reckoned half yearly.
16000((1+.05/2)^3 - 1 - .05*3/2) = 30.25
Now, if you meant 3 1/2 years, fix it up.
compound interest 650 in 5years at 4pac per anum
To find the difference between the simple interest and compound interest, we need to calculate the simple interest and compound interest separately.
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.
To find the difference between the simple interest and compound interest on a given principal amount, you need to calculate both the simple interest and compound interest separately.
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.