what rate of annual simple interest is equivalent to 9% per annum compounded semi-annually for 3 years
rate = (1.045)^2
= 1.092025
or 9.2025 %
since you want the annual simple interest, the 3 years is irrelevant, all we have to do is look at a 1 year period
looked at it again....
amount after 3 years at the compound interest
= 1.045^6
= 1.30226
so interest on $1 is .30226
using I = PRT
.30226 = 1(r)(3)
r = .10075
the annual simple interest is 10.075%
check:
Assume we have $100
amount after 3 years using the compound interest
= 300(1.045)^6 = 130.23
amount using simple interest of 10.075%
= 100 + 100(.10075)(3) = 130.23
YEAHHH
To find the equivalent rate of annual simple interest, we need to determine the interest rate that would give the same amount of interest over the same period, assuming simple interest.
We know that the compound interest rate is 9% per annum compounded semi-annually for 3 years.
To convert the compounded interest rate to a simple interest rate, we can use the formula:
Simple Interest Rate = (2 * Compound Interest Rate) / (1 + Compound Interest Rate)
Let's calculate it step-by-step:
1. Convert the compounded interest rate to decimal form:
Compound Interest Rate = 9% = 0.09
2. Apply the formula to find the equivalent annual simple interest rate:
Simple Interest Rate = (2 * 0.09) / (1 + 0.09)
= 0.18 / 1.09
≈ 0.1651 or 16.51%
Therefore, the equivalent rate of annual simple interest is approximately 16.51% per annum.
To find the equivalent rate of annual simple interest, we can use the formula:
A = P(1 + rt)
Where:
A is the future value of the investment
P is the principal amount
r is the annual interest rate
t is the time period in years
In this case, "A" represents the future value of the investment after 3 years, compound semi-annually at a rate of 9% per annum. We can assume the principal amount is 1 for simplicity.
First, let's calculate the future value of the investment using the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
n is the number of compounding periods per year
In this case, the investment is compounded semi-annually, so n = 2.
A = (1 + 0.09/2)^(2*3)
A = (1 + 0.045)^6
A = (1.045)^6
A ≈ 1.2839
Now, let's substitute the values into the simple interest formula and solve for the interest rate (r):
1.2839 = 1 + r*3
0.2839 = r*3
r ≈ 0.0946
Therefore, the rate of annual simple interest that is equivalent to 9% per annum compounded semi-annually for 3 years is approximately 9.46%.