Question

Kate is in the 15% tax bracket and has $29,000 available for investment during her current tax year. Assume that she remains in the same tax bracket over the next 11 years, and determine the accumulated amount of her investment after taxes if she puts the $29,000 into the following. (Round your answers to the nearest cent.)

(a) a tax-deferred annuity that pays 4%/year, tax deferred for 11 years

(b) a taxable instrument that pays 4%/year for 11 years
Hint: In this case, the yield after taxes is 3.4%/year.

Answer 1

For case a)

The amount invested is 29,000 in a tax-deferred instrument. In this case, we need to calculate future value with rate of interest 4% and years = 11

FV after 11 years = 29,000 * (1+4%)^11

FV after 11 years = $44,644.1676 and this amount will be taxed at 15% after 11 years, hence, the net value obtained = 44,644.1676 * (1-15%)

= $37,947.5425

Case b:

Effective yield if invested in taxable instrument = 4%*(1-15%) = 3.4%

Now, Future Value in 11 years with 3.4% return = 29000*(1+3.4%)^11

= 29000* (1.44452787)

=41,891.3083

Hence, option b is preferable