00:01
So in the given question, we are told to find the annual interest rate related to an amount which is given as $5 ,000, which will grow into an amount of $6 ,200.
00:19
And it is given that the interest is compounded quarterly in this case.
00:24
The interest is compounded quarterly and it is done for eight years.
00:37
So we are told to find the annual interest rate related to this case.
00:42
That is when an amount of $5 ,000 grows into $6 ,200 in eight years when the interest is compounded quarterly.
00:52
So we can use the formula for compound interest which is given.
00:57
As the accumulated amount which is the $6 ,200 is equal to p which is the initial investment which is also called the principal amount times 1 plus r where r is the annual interest rate divided by n which is the number of times the interest is compounded in an year and 1 plus r by n is raised to the power n times.
01:28
T where t is the time in years.
01:31
So we have all the values which is the accumulated amount that is $6 ,200.
01:38
The principal amount which is $5 ,000 and it is said that the interest is compounded quarterly which means the number of times the interest is compounded is 4 and we also have the time which is 8 years.
01:54
So the annual interest rate related to this case would be equal to r is the is r which we are going to find.
02:05
So let's substitute these values...