Question

You have won the local lottery. You have been awarded a 41-payment, constant growth annuity. The first paument is at year 0 and is equal to 10,000. Each subsequent payment will be paid in 6 month intervals, with the final payment at year 20. Further, payments will grow at a constant growth rate of 4 percent. The appropriate discount rate for this constant growth annuity is a nominal annual rate of 6.4 percent, with monthly compounding. Given this information, determine the value of, at year 0, of this constant growth annuity.

Answer 1

The cash flows constitute a growing annuity due of 41 semi annual payments

Semi annual rate equivalent to 6.4% compounded monthly is 3.242971% as follows:

Present Value of the growing annuity due PVA= P/(r-g)*(1-((1+g)/(1+r))^n)*(1+r)

Where

P= First payments (given as $10,000),

n= Number of payments (given as 41),

r= Rate of interest per period in decimals (0.032429713 as above)

and g= Growth rate per period in decimals (0.02)

Plugging the inputs, Present Value of the annuity

= 10000/(0.032429713-0.02)*(1-((1+0.02)/(1+0.032429713))^41)*(1+0.032429713)

= $325,108.48