00:01
In this question, we are given that laura deposits $2 ,000 in an account that has an annual interest rate of 3 .96 percentage, but that is compounded monthly that we have to take care.
00:11
So how much interest will she earn at the end of one month? so first, what is the formula for the compound interest? so the amount amount is actually equal to principal times 1 plus r over k over 100 raised to the power of kt, where p is the amount.
00:30
The principal amount which is given as $2 ,000 in this case.
00:34
R is the annual interest rate which is given as 3 .96 definitely in percentage.
00:40
T is the value of time which is which we have to write in years because the rate of change the rate is also given in years.
00:49
So actually it is one month but we are going to write time as one over 12 years because one month is nothing but one over 12 year.
00:56
And k is the compounding rate so it is compounded monthly the value of k is 12 because it should be compounded it should be taken 12 times because there are 12 months in a year so it's only a matter of substituting all these values now so the value of the amount comes out as the principal which is 2000 1 plus the rate which is 3 .96 over the value of k which is 12 and there is 100 already raise to 12 times 1 over 12 because the value of t is 12 and k is 1 over 12.
01:32
So the value of this simplifies to 2 ,000 times 1 plus 3 .96 over 12 times 100 is 200 raised to 1 because 12 and 1 over 12 are just cancers...