Question

9. Calculate the PV an annuity that pays $2000 at the end of each year from year 12 through year 44, given an appropriate discount rate of 8%. Answer: $9876.22.

Answer 1

First Let's Calculate PV of an Annuity that pays $1 for next 44 years at Discount Rate of 8%p.a.

PVIFA for 44 Years @ 8% = 12.0771

But we receive annuity only from Year 12. So let's calculate PV of an Annuity that pays $1 for next 11 years at Discount Rate of 8% p.a.

PVIFA for 11 years @ 8% = 7.139

As we don't receive annuity for first 11 years, we can subract it from PVIFA for 44 years, to get our desired result.

Therefore PVIFA of Annuity that pays $1 from year 12 through year 44 @ 8% = 12.0771 - 7.139 = 4.9381

Hence, PV of Annuity that pays $2000 from year 12 through year 44 @ 8% = 4.9381*2000 = $9876.2