Answer:
Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 15-year annuity is $750,000 and the annuity earns a guaranteed annual return of 6.85%. The payments are to begin at the end of five years.
What is the amount of the annuity purchase required if you wish to receive a fixed payment of $100,000 for 25 years
Explanation:
present value of the ordinary annuity = $750,000
n = 15
interest rate = 6.85%
in order to calculate the annuity payment, we can use the formula for the present value of an annuity:
PV = annuity payment x annuity factor
annuity payment = PV / annuity factor
- PV = $750,000
- annuity factor 6.85%, 15 periods = 9.19484
annuity payment = $750,000 / 9.19484 = $81,567.49
since 6.85% is not a full number, it is hard to find annuity tables that contain it, but we can always search for annuity table calculators that can help us determine the annuity factor.
for the second question, we need to determine the PV of the ordinary annuity
PV = annuity payment x annuity factor
- annuity payment = $100,000
- annuity factor 6.85%, 25 periods = 11.81276
PV = $100,000 x 11.81276 = $1,181,276
