convert an effective anual interest rate 8% compounded annually to a nominal interest rate of 11.5% p.a compounded monthly correct to one decimal place
11.5% p.a compounded monthly
let that annual rate be i
1 + i = (1 + .115/12)^12
1 + i = 1.121259...
i = appr .1213 or 12.13%
So the first rate is 8% per annum compounded annually, the other is 12.13% per annum compounded annually.
You cannot convert one to the other.
That's like saying: make 5 equal to 9
To convert the effective annual interest rate of 8% compounded annually to a nominal interest rate of 11.5% p.a compounded monthly, follow these steps:
Step 1: Convert the nominal interest rate from an annual rate to a monthly rate.
To do this, divide the annual rate by the number of compounding periods per year:
Monthly interest rate = 11.5% / 12 = 0.95833%
Step 2: Calculate the effective annual interest rate corresponding to the monthly rate.
To find the effective annual interest rate, use the formula:
Effective Annual Interest Rate = (1 + Monthly interest rate)^Number of compounding periods - 1
In this case, the number of compounding periods is 12 (monthly compounding), so the formula becomes:
Effective Annual Interest Rate = (1 + 0.95833%)^12 - 1
Step 3: Calculate the effective annual interest rate in decimal form.
Convert the percentage to a decimal by dividing it by 100:
Effective Annual Interest Rate (in decimal form) = (1 + 0.95833%)^12 - 1 / 100
Step 4: Calculate the effective annual interest rate in percentage form.
Multiply the result from step 3 by 100 to convert it back to a percentage:
Effective Annual Interest Rate = Effective Annual Interest Rate (in decimal form) * 100
By solving the equation in step 4, we find:
Effective Annual Interest Rate ≈ 12.6853%
Therefore, the nominal interest rate of 11.5% p.a compounded monthly is approximately equivalent to an effective annual interest rate of 12.7% when compounded annually.
To convert an effective annual interest rate to a nominal interest rate compounded monthly, you can use the following formula:
Nominal interest rate = [(1 + Effective interest rate / Number of compounding periods)^(Number of compounding periods)] - 1
In this case, the effective annual interest rate is 8% and it is compounded annually. The nominal interest rate is 11.5% compounded monthly.
First, let's calculate the number of compounding periods per year:
Number of compounding periods = 12 (since it is compounded monthly)
Next, substitute the values into the formula and calculate the nominal interest rate:
Nominal interest rate = [(1 + 0.08 / 12)^(12*1)] - 1
= [(1 + 0.0066667)^(12)] - 1
= (1.0066667)^12 - 1
≈ 0.080847 - 1
≈ 0.080847
To express the nominal interest rate as a percentage correct to one decimal place, multiply the result by 100 and round to one decimal place:
Nominal interest rate = 0.080847 * 100 ≈ 8.1%
Therefore, the nominal interest rate of 11.5% p.a compounded monthly is approximately equivalent to an effective annual interest rate of 8.1% correct to one decimal place.