Compute effective rate of interest where nominal rate is 8% compounded quarterly?
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Why did the nomad become an accountant? Because he wanted to compute the effective rate of interest!
To calculate the effective rate of interest when the nominal rate is 8% compounded quarterly, we'll need to use the formula:
Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods)) ^ Number of Compounding Periods - 1
Using this formula, let's break it down:
Nominal rate: 8%
Number of compounding periods: 4 (since it's compounded quarterly)
Plug these numbers into the formula:
Effective Rate = (1 + (0.08 / 4)) ^ 4 - 1
Effective Rate = (1 + 0.02) ^ 4 - 1
Effective Rate = (1.02) ^ 4 - 1
Effective Rate = 1.0824 - 1
Effective Rate = 0.0824
So, the effective rate of interest is approximately 8.24%. Keep in mind that this is rounded off to two decimal places.
To compute the effective rate of interest when the nominal rate is 8% compounded quarterly, you need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal (initial amount of money)
r = the nominal interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the nominal interest rate is 8% (0.08 in decimal form), the compounding is done quarterly (n = 4), and we want to find the effective rate for one year (t = 1).
The formula can be simplified to:
A = P(1 + r/n)^(nt)
A = P(1 + 0.08/4)^(4*1)
A = P(1 + 0.02)^4
A = P(1.02)^4
So to calculate the effective rate, we need to solve for (1.02)^4.
(1.02)^4 = 1.082432
Now, to find the effective rate, subtract 1 from the result:
Effective rate = 1.082432 - 1 = 0.082432
Convert this to a percentage:
Effective rate = 0.082432 * 100 = 8.2432%
Therefore, the effective rate of interest when the nominal rate is 8% compounded quarterly is approximately 8.2432%.
Effective rate = (1+r/4)^4 -1
= (1+0.08/4)^4-1
=(1.02)^4-1
= 16.98%