00:01
In this problem of exponential function, we have given that find the future value and the interest earned if this is here the amount is the principal amount is given as if $56 ,780 is invested at rate of this rate is 5 .3%.
00:22
The first compounded quarterly for 23 quarters.
00:26
So first compounded quarterly and the second case is here.
00:35
That is continuously for 15 years.
00:42
For 15 years.
00:46
And now we are taking first case that is here, rate is equal to this is, rate is equal to this is 0 .053.
00:57
And now we have given that compounded quarterly and first case, we have to find this is quarterly for 23 quarters.
01:06
So this is here quarterly for 23 quarters.
01:15
So first we have to find the rate that is the quarterly rate so this would be r divided with 4.
01:20
So this would be 0 .0 .0 .053 divided with 4 and the principle would be here.
01:31
Principal is same that it equals to 56 ,780 dollar.
01:38
So the amount would be after 23 quarter that is a is equal to p 1 plus rate rate would be here 0 .0 .0 .0.
01:45
0 .053 divided with 4 and number of quarter that is 23 and now we have to solve it.
01:51
So p is equal to 56 ,780 multiplied with this would be 1 plus 0 .053 divided with 4 is equal to 0 .0132 so this would be here 0 .01 325 this is 325 to the power 23.
02:13
And now when we evaluate it so this would be here 56 ,000 780 multiplied with this would be 1 .3537 so this would be 1 .355 this would be 1 .35 this is 3537 and now this is multiplied with 56 ,000 780 equals to 76 ,000 so this would be in dollar so this would be 76 ,000 855 .9494 so this is the amount amount after 23 quarters and now we have to find the interest earned so interest earned is equal to a minus p so now put the value so this is equal to 76 ,855 .94 minus 56 ,780 equals to 20 ,000 and 75 so this would be dollars 20 ,000 and 75.
03:12
So this would be dollars 20 ,000 and 75 .94 so this is the interest earned...