Question

An annuity immediate has 40 initial quarterly payments of 20 followed by perpetuity of quarterly payments of 25 starting in the eleventh year. Find the present value at 4% convertable quarterly.

Answer 1

year 0 to year 10 payments of 20 every quarter from year 11 continuous payment of 25 per quarter (perpetuity)

we can solve the problem by

step 1 :bringing the 10 years equal inflows or payments to year zero by multiplying present value interest factor annuity(PVIFA) because equal payments at an equal interval of time.

and step 2 : bring the perpetuity payments to the end of year 10 then convert the value to present value of the year 0

step 1

discounting rate 4% convertable quartarly means it is per year and we should change to quarter thet is 4/4 = 1%

present value of first 10 years income is

= 20 *PVIFA at 1% for 40 periods ( each year contain 4 periods for 10 years 40 periods )

= 20*32.835 ( from calculator value 1/1.01^40 and press GT )

=656.7

step 2

quarter payment perpetuity 25

present value = 25/0.01= 2500 ------------------ > at end of year 10 then bring it to year 0 by multiplying with PVIF at 4% for 10 years we are doing directly no need to use quarterly

= 2500*0.676 ( from PVIF table at 4% for 10 period )

= 1696 ---------------> pv at year zero

total present value is 656.7+1696= 2352.7