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Homework answers / question archive / Determine the difference between the present value of a $10,000 twenty-year annuity earning 10% interest compounded annually versus a $10,000 twenty-year growing annuity earning 10% interest compounded annually and having a 3% annuity growth rate
Determine the difference between the present value of a $10,000 twenty-year annuity earning 10% interest compounded annually versus a $10,000 twenty-year growing annuity earning 10% interest compounded annually and having a 3% annuity growth rate.
Computation of the present value of annuity:-
PV of annuity = Annuity*((1-1/(1+rate)^n)/rate)
= $10,000*((1-1/(1+10%)^20)/10%)
= $10,000*8.5136
= $85,135.64
Computation of the present value of growing annuity:-
PV of growing annuity = Annuity*(1-((1+g)^n)*((1+rate)^-n))/(rate-g)
= $10,000*(1-((1+3%)^20)*((1+10%)^-20))/(10%-3%)
= $10,000*10.4505
= $104,504.72
Difference = PV of growing annuity - PV of annuity
= $104,504.72 - $85,135.64
= $19,369.09
