00:04
So we're given that an investor deposits wants to withdraw 2 ,500 at the end of every year, right, for a period of 10 years at a discount rate of 12 %, right? and we want to know how much you should deposit now so that you can have this amount of cash available, right? so the first case is when the investment is made at the end, right? so my formula for my present value, that is how much he should.
00:35
Deposit now is basically the present value of all my cash flows.
00:39
So it's an annuity, right? and the annuity is of amount 2 ,500 yearly, right? i need to discount this.
00:48
So i'm going to use the formula 1 minus 1 plus i which is 1 .1 .2 to the power minus 10 because i'm discounting over my i which is 0 .1 .2.
01:01
Right when i do this i get that my answer is 12 ,147 .98 right then for the second case when this when this investment is made at the beginning it's a little bit different sorry in the beginning right so in when it's being made in the beginning right so in when it's being made in the beginning my pv is 2 ,500 right times one minus 1 .1 .12 to the power minus 10 over 0 .12 it's almost like the first formula only that we need to accumulate just for one more period right when i do this my answer is 13 000 605 .74 now i just want to draw some simple number lines to explain the difference in these formulas right so when we are using when we are making an investment at the end of every year right so let's say this is zero this is one this is two this is three and so on and this is my end right right if i'm making an investment at the end of every year it means that i'm making an investment here studying from the end of year one right since i'm studying here i make an investment at the end here i'm making an investment here and here and so on up to time in right but for when i'm making an investment at the beginning of the it means that i am making an investment here, investment here, investment here, investment here, and then i end at time n minus one...