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# The Value of Tax Deferral

Many provisions of tax law permit a taxpayer to defer the paying of taxes on "gain" or income until some event has occurred, often the sale of an underlying asset. This Demonstration shows the value of tax deferral to a taxpayer and the corresponding loss to the government imposing the tax. The basic concept is that a taxpayer invests a dollar. The dollar earns interest at a user-specified interest rate with a user-specified compounding period, such as 3% compounded quarterly. Absent tax deferral, the taxpayer pays tax on the interest earned since the last investment at a user-specified rate at each assessment period, conventionally one year. The taxpayer then reinvests whatever is left and the process recurs for a user-specified duration. With tax deferral, however, the taxpayer does not pay tax until the end of a user-specified deferral period, whereupon the tax is imposed on all interest earned to date. The rate of tax at the end of the deferral period is generally the same as it would have been had no deferral existed, although, with an advanced control, the user can specify a different rate of tax. Use of this advanced control might be appropriate where, at the end of deferral period, the marginal tax rate faced by the taxpayer has changed, possibly as a result of retirement and loss of other sources of income.
This Demonstration responds to user input with a graph showing the value of the investment with and without tax deferral. An inset grid also shows the present value of the taxes paid with and without tax deferral.

### DETAILS

Snapshot 1: when interest rates are low, tax rates are low and the deferral period is relatively short; deferral has minimal effect
Snapshot 2: when interest rates are high, tax rates are high and the deferral period is relatively long; deferral has maximal effect
Snapshot 3: reducing the tax rate at the time of deferral increases the potency of tax deferral
To the author's knowledge, the closed-form expressions for the value of tax deferral underlying this Demonstration and derived with a single line of Mathematica using RSolve have not previously been published.

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