# TVM Question

Given a 5 percent discount rate, find the present value of a four-year ordinary annuity of \$100 per year starting in Year 1 as the difference between the following two level perpetuities: Perpetuity 1 - \$100 per year starting in Year 1 (first payment at t=1) Perpetuity 2 - \$100 per year starting in Year 5 (first payment at t = 5) A) \$354.60 B) \$345.20 C) \$394.56

A

I agree. A for PP1 = A/R=100/0.05=2000 at t=1 for PP2 = A/R=100/0.05= 2000 at t=5 . discounting back to n=4 will give PV=1645.4

A

A PV of 2nd,3rd and 4th year payments = 259.356 for the first year payment difference between perpetuities= 100 PV for year 1 = 100/1.05 = 95.238 Total PV for annuity= 259.356 + 95.238 =354.6

patel.kartikv Wrote: ------------------------------------------------------- > I agree. A > > for PP1 = A/R=100/0.05=2000 at t=1 > > for PP2 = A/R=100/0.05= 2000 at t=5 . discounting > back to n=4 will give PV=1645.4 Exactly correct.

Why do they make that kind of question? I know that an annuity could be presented by the difference between a perpetuity and a deferred perpetuity. But you could simply use the calculator and enter n=4, i/y = 5, pmt = 100 to get the result.

To test your understanding of how differing annuities can be used to achieve a similar result.