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

Finance Dec 24, 2020

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.

Expert Solution

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

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