Question

Kenneth was considering whether to place 10,000 in a tax-deferred annuity or a tax-free municipal bond. Assume the municipal bond returned 5% a year and the tax-deferred annuity 6%. Calculate approximately how long he would have to hold the annuity, so that, if he withdrew the money and paid taxes on it, he would come out ahead. His marginal tax rate is 35%.

Answer 1

Tax deferred annuity future value=10000*1.06^t-(10000*1.06^t-10000)*35%

Municipal bond future value=10000*1.05^t

Hence,

10000*1.06^t-(10000*1.06^t-10000)*35%>=10000*1.05^t

=>1.06^t-(1.06^t-1)*0.35-1.05^t>=0

=>t>=40.0921

It will take 41 years