Rate of interest

[Saumyojit]

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

What is the meaning of the question?


If 6 percent is half yearly.
Then 1 year annually would be 2*6=12 percent

 

[Saumyojit]

@Dr.Peterson
@Jomo
Please reply

 

[Steven G]

It clearly states that the rate is 6% per annum so why would you say 6% is for half a year? Why would you say that 12% per year (ie 12% per annum)???????

 

[MarkFL]

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

What is the meaning of the question?


If 6 percent is half yearly.
Then 1 year annually would be 2*6=12 percent

I would write:

[MATH]100\%\left(\left(1+\frac{0.06}{2}\right)^2-1\right)=6.09\%[/MATH]
And so we find that the effective rate for 6% APR compounded twice per year is 6.09%.

 

[Dr.Peterson]

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

What is the meaning of the question?

Let's try to make this very simple, since you evidently don't have a textbook that teaches you the concepts. (You really need to find one.)

I assume, first, that "payable half-yearly" means it is compounded twice a year.

The interest rate is 6% per annum (that is, per year). So the interest for the first half year is 6/100 times principal (which we can take as 1) times 1/2 year, that is, 0.03. Right?

Now we add that to our principal to get 1.03 as the principal for the second half year. The interest for this second half year is therefore 6/100*1.03*0.5 = 0.0309.

Our total interest for the year is therefore 0.03+0.0309 = 0.0609. What percent is that of the principal, 1? 6.09%.

That is what is meant by effective annual rate of interest: the rate of simple interest that would result in the same total amount after 1 year.

 

[Saumyojit]

why this sum is not of si but ci?

 

[Saumyojit]

@
Dr.Peterson
why this sum is not of si but ci?
I did not understand the question ? if they have given per annum interest 6 percent then why they are asking again effective annual rate of interest?

 

[MarkFL]

@
Dr.Peterson
why this sum is not of si but ci?
I did not understand the question ? if they have given per annum interest 6 percent then why they are asking again effective annual rate of interest?

That is what is meant by effective annual rate of interest: the rate of simple interest that would result in the same total amount after 1 year.