Question

c. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 25-year annuity is $1.1 million and the annuity earns a guaranteed annual return of 11 percent. The payments are to begin at the end of six years.

Answer 1

Given about a 25-year annuity that will start paying in 6 years from now.

PV of annuity = $1100000

interest rate = 11%

So, Value of annuity at the end of year 5 using compounding is

Value at year 5, PV5 = PV*(1+r)^t = 1100000*1.11^5 = $1853563.97

So, now it is an ordinary annuity with PV = $1853563.97 and payment starting at the end of year. So its annuity formula is

PMT = PV*r/(1 - (1+r)^-t) = 1853563.97*0.11/(1 - 1.11^-25) = $220092.63

So annual cash flow = $220092.63