Question
Find the compound interest on ksh21000 in 3 years at a ratio of 20% p.a compounded semiannually.
Answers
GPT 3.5
To find the compound interest on Ksh21000 in 3 years at a rate of 20% p.a compounded semiannually, we first need to calculate the semiannual interest rate.
The annual interest rate is 20%, so the semiannual interest rate is 20%/2 = 10%.
Now, we can use the compound interest formula to find the compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (Ksh21000)
r = the annual interest rate (20% or 0.2)
n = the number of times that interest is compounded per year (2 for semiannual)
t = the number of years the money is invested/borrowed for (3 years)
Plugging in the values:
A = Ksh21000(1 + 0.1/2)^(2*3)
A = Ksh21000(1.05)^6
A = Ksh21000 * 1.340097
A = Ksh28122.02
Now, we can calculate the compound interest:
Compound interest = A - P
Compound interest = Ksh28122.02 - Ksh21000
Compound interest = Ksh7122.02
Therefore, the compound interest on Ksh21000 in 3 years at a rate of 20% p.a compounded semiannually is Ksh7122.02.
The annual interest rate is 20%, so the semiannual interest rate is 20%/2 = 10%.
Now, we can use the compound interest formula to find the compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (Ksh21000)
r = the annual interest rate (20% or 0.2)
n = the number of times that interest is compounded per year (2 for semiannual)
t = the number of years the money is invested/borrowed for (3 years)
Plugging in the values:
A = Ksh21000(1 + 0.1/2)^(2*3)
A = Ksh21000(1.05)^6
A = Ksh21000 * 1.340097
A = Ksh28122.02
Now, we can calculate the compound interest:
Compound interest = A - P
Compound interest = Ksh28122.02 - Ksh21000
Compound interest = Ksh7122.02
Therefore, the compound interest on Ksh21000 in 3 years at a rate of 20% p.a compounded semiannually is Ksh7122.02.