Question

I am perplexed. The problem I am working on (using financial package in R) is ,

Question : How much money must Carol deposit every year starting 1 year from now at 5.5 % per year in order to accumulate $6000 seven years from now?

My correct solution is :

> 6000/usfv(5.5,7)
[1] 725.7865

I think this should also work… but does not:

> tvm(i=5.5,n=7,fv=-6000,pmt=NA,pyr=1)

Time Value of Money model

   I% #N PV    FV    PMT Days #Adv P/YR C/YR
1 5.5  7  0 -6000 687.95  360    0    1    1

I am getting a difference PMT amount. Does anyone have an insight in why I a getting the difference

Answer 1

Trying to check the numbers manually and playing with the indices helped me understand what is going on:

p1 <- 6000 / usfv(5.5,7)

matches the expectation that

sum(p1*(1 + 5.5/100)^(0:6))
# [1] 6000

For

p2 <- tvm(i=5.5,n=7,fv=-6000,pmt=NA,pyr=1)[1,"PMT"]

you have to change the time of the cashflows to get

sum(p2*(1 + 5.5/100)^(1:7))
# [1] 6000

In other words, usfv assumes cashflows at times 1 through 7 while tvm assumes cashflows at times 0 through 6 (and both functions assume future value is at time 7.)

P.S.: when testing my intuition, I also found that both functions cannot work with a zero interest rate (one returns NaN, the other errors out.) These on top of the useless documentations: I would not recommend that package…