00:01
Hello everyone a given function r of t this is the function of a continuous income stream and here the given that is 0 less than equals to t less than equals to 5 that means t is between 0 and 5 or equals to 0 and 5 and here rate of interest is given that is 10 percent so they are saying first e to compute to find the value of t v tv that means a total back so we know if we required a total value so here a and b already provided because t is between 0 and 5.
00:42
So i will take a formula integration is going from a to b r of t d t.
00:52
Now let us put the value here so integration is going from a to b.
01:00
A is equal to 5 u .a is equal to 0 and b is equal to 5.
01:04
R of t so equation is already provided so this is equal to 40 ,000 plus 2 ,000 t and with respective t that is dt so let us integrate them so i'm getting this is equal to the integration of 40 ,000 this is equal to 40 ,000 t and integration of 2000 so the t that is 2 ,000 t squared by 2 and this is of the type definite integration so we will write down 0 to 5 here so here we can put the value of 5 because upper limit is 5 so for t000 multiplied by 5 so i'm getting here that is 2 lakh plus here 2 ,000 divided by 2, so this become 1 ,000.
02:16
So i'm writing 1 ,000 and t square that is 5 square that is 25.
02:21
So 25 multiplied with 1 ,000.
02:24
So this become 25 ,000.
02:29
Next minus upper limit when i lower limit when i apply.
02:33
So this become 0.
02:35
Now, so 2 lakh plus 25 ,000.
02:39
So this is equals to 2 lakh.
02:43
So this is nothing but our total value.
02:48
So i will write down at last.
02:51
Therefore total value is equals to 2 lakh 25 ,000.
03:05
Next as well as we required this fv.
03:10
Fv stands for future value.
03:12
So let us compute fv here.
03:17
Fv.
03:19
So here for fv we will use a four formula, integration is going from a to b, r of t, e raise to the power, r in a bracket, b minus t and dt.
03:41
Here rate of interest is t that is rate of interest and this is equal to the given like 10%.
03:49
So 10 % that means 10 divide by 100.
03:51
That means i can take here 0 .1.
03:54
So t is equal to 0 .1 here.
03:56
Here...