Time Value of Money

[praveenraj]

If we want to compare both this rates how can we do that as we cant compare $15000 for 15 years ?

 

[Parmeshwar]

Find out the present value of 15000 in Today's term 15000/(1.09)^5 (if I don't assume continuously compounded) otherwise 15000* exp(-0.09*5)


For the 2nd situation better use ur financial calculator

PMT 1000 , FV 0 ,I as 9 N as 15 CPT PV

That will be enough to say what u will choose

 

[praveenraj]

is there a way we can convert 15000 to 15yrs in line with $1000 annuity for 15 year

 

[Parmeshwar]

Yes there is nothing wrong with ur thought process....the main thing is same time frame it could be either present future and any interval between future and present

 

[Parmeshwar]

U may also find the value of annuity at time t=5

And that can be compared directly with 15000

 

[praveenraj]

Got what you were saying how can we find Fv of annuity 1000 for 5 yrs

 

[praveenraj]

Got what you were saying how can we find Fv of annuity 1000 for 5 yrs? according to the methods you mentioned above 15000 was a better option.

 

[David Harper CFA FRM]

@praveenraj See https://www.investopedia.com/retirement/calculating-present-and-future-value-of-annuities/ for both PV and FV formulas; i.e.,

• The PV of the ordinary annuity (if the discount rate is 0.09) = C* [1-(1+i)^-n]/i = 1000*(1 - 1.09^-15)/0.09 = $8,060.7; i.e., less than FV = 15000/1.09^15
• The FV of the ordinary annuity (if the discount rate is 0,09) = C* [(1+i)^n-1]/i = 1000*(1.09^15-1)/0.09 = $29,361; i.e., also less than FV = 15000*1.09^(15 - 5)