00:01
Hello students, we are given a question here.
00:02
What is the present value of deferred annuity with a different period of 17 years at 6 .7 % compounded semi -annually, followed by a 10 -year annuity due paying $1 ,250 every month at 4 .78 percentage compounded semi -annually.
00:22
So first of all, we are supposed to know that here.
00:25
The present value of deferral annuity present value of a deferred annuity can be written as equal to its formula is p is equal to one plus j times off okay one plus j and whole power is minus km times r and times here we can say that one minus one plus jay whole power is minus empty and whole divided by j okay students so now here we can say that the variables are like here we can write where okay students what is j we will start with j j j is nothing but equal to 1 divided by m it means interest rate per conversion period which is nothing but equal to here we can say that the interest rate per per per conversion period okay students so here we are supposed to know that the sorry actually it is i okay interested so basically we can say that i is given as here 6 .7 percentage but the compounded semi -annual it means divided by 2 so basically what we will get here it will be 3 .35 percentage now i is given as here 6 .7 percentage students i is 6 .7 percentage which is the interest rate required and now here second thing is like m is nothing but the number of compounding period okay so here m is given as equals to 2 we have recently calculated k what is k is nothing but the period of deferral period of a deferral now we can check here check here period of deferral it is nothing but equal to 17 years so we can mention here 17 years.
02:37
Now r is nothing but the regular payment.
02:40
R is regular payment which was nothing but equal to $1 ,250.
02:51
Okay, students.
02:53
And now here we are supposed to know that t is nothing but the time of actual payment.
02:58
T is a time of a, here we can say that actual payment.
03:03
Students actual payment so it is given as equal to obviously what we are given here time of actual payment is we can check here 10 years so we can even mention below 10 years now we can put all those values in our particular formula so here we can just mention that the p is equal to see here we can write p is equals to 1 plus what was the that 1 plus j, k students, so j is a 3 .35 percentage, it means 3 .35 and divided by 100.
03:43
When we convert percentage in decimal, okay, and whole power is minus km.
03:47
So k is 70 and m is 2.
03:51
Okay, students, times r.
03:54
So r is $1 ,250 and whole times of a here 1 minus of 1 plus, again, j, so 3 .34...