why the FV=0 when calculate the PV of an ordinary annuity problem.

on Page 73 of Scheweser Notes 2018 book 1

Example : PV of an ordinary annuity.

What is the PV of an annuity that pays $200 per year at the end of each of the next 13 year, given a 6% discount rate?

the answer is:

N=13, I/Y=6, PMT=-200, FV=0, CPT>PV=$1770.54

why FV=0? does it mean the future value of money is ZERO?

To my understanding FV stands for the future value of money.

so why the investor invests money for nothing…?

Can anybody help to explain the reason please?

The investor would pay $1,770.54 today to receive 13 annual cash inflows of $200 for 13 years.

For instance, at the end of the first year, the PV will grow with interest to $1,876.77. The investor will then receive the first $200, which will then reduce the account balance to $1,676.77. If we repeat this process year by year, then at the end of year 13, there will be exactly $200 in the account to pay the last cash flow.

FV = 0 means that there isn’t an extra amount (above PMT) paid on the last payment date.

For example, if you own a 2-year, 6% coupon, $1,000 par bond, then there are 4 payments:

  • $30 6 months from today
  • $30 1 year from today
  • $30 18 months from today
  • $1,030 2 years from today

The extra $1,000 2 years from today is FV (= 1,000). It’s an additional amount on top of the PMT (of $60).