I have a question though. I tried to come up with the formula for future value of annuity using your method 1. However, I just can't get it right. I've arrived at P[(1+r)/1 -1]= A [1 - (1+r)^(n-1)] and then try to solve for P. I tried multiple times to simplify the current version but none of the derivations gets me the most simplified version. Could you explain it, please? Do I have to use geometric sequence to derive the formula for FV of annuity? Thank you so much for your help Professor.
Let P(t) denote the present value (at the time 0) of the amount 1 that is to be received at the time t. Show that r(t) is a nondecreasing function of t if and only if P(αt) ≥ (P(t))^α
The top line has P = A/(1+i) + ... + A/(1+i)^n. If I subtract A/(1+i)^n from both parts of this equation I get P - A/(1+i)^n = A/(1+i) + ...+ A/(1+i)^{n-1}. Thus when I see A/(1+i) + ...+ A/(1+i)^{n-1} in the second line, I can replace it with P - A/(1+i)^n.
I really admire people who is good at math, ty.
5:04 you told me to pee on both sides of the equation, but it didn’t solve my problem
Thank you,you saved my test
Thank you for simplifying this.
I have a question though. I tried to come up with the formula for future value of annuity using your method 1. However, I just can't get it right. I've arrived at P[(1+r)/1 -1]= A [1 - (1+r)^(n-1)] and then try to solve for P. I tried multiple times to simplify the current version but none of the derivations gets me the most simplified version. Could you explain it, please? Do I have to use geometric sequence to derive the formula for FV of annuity? Thank you so much for your help Professor.
thank you very much. It is very helpfull. Hello from Turkey:)
excellent video!
5:00 -sign ??
@@CALMWAVESFREEMUSIC it was used to cancel out the extra number(the last number) that P has.
Let P(t) denote the present value (at the time 0) of the amount 1 that is to be received at the time t. Show that r(t) is a nondecreasing function of t if and only if P(αt) ≥ (P(t))^α
Can I get a video for future value?
Great job dude
Great video!
thank you so muchh !! you've been a great help !
5:00 where did this - sign came from ....?
The top line has P = A/(1+i) + ... + A/(1+i)^n. If I subtract A/(1+i)^n from both parts of this equation I get P - A/(1+i)^n = A/(1+i) + ...+ A/(1+i)^{n-1}. Thus when I see A/(1+i) + ...+ A/(1+i)^{n-1} in the second line, I can replace it with P - A/(1+i)^n.
Thanks!
Thanks man!
Yup. I'm still an idiot. 🙄🔫