gemini070900
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- Joined
- Feb 9, 2010
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# 34
Compare three kinds of investments for retirement, an ordinary after tax investment, a tax deferred investment (annuity or IRA), and a Roth IRA. Let an investment earn interest at a steady annual yield r and let your income (what ever year you receive it) be taxed at rate r.
A) Ordinary after-tax investment: Explain why if you earn $ E, pay taxes on it, let what remains earn interest, and pay tax each year on that years interest, the $ E grows after n years to $ E(1-r)x(1+r(1-r)n.
B) Ordinary IRA: Explain why if you earn $ E, defer taxes on it, let what remains earn interest, and defer taxes on all the interest, then the E grows after n years to $ E(1+r)n(1-t).
C) Roth IRA: Explain why if you earn $ E, pay taxes on it, let what remains earn interest, and pay no taxes on all the interest, the $ E grows after n years to $ E (1-r)(1+r)n.
D) Which investment gives the best return after n years?
E) If your marginal tax rate (the rate you pay on one more dollar of income) is lower in one year than the tax rate you expect to pay in retirement, what kind of retirement investment is better for you that year?
If you have a windfall one year and your marginal tax rate is higher that year than the tax rate you expect to pay in retirement, what kind of retirement investment is better for you that year?
Compare three kinds of investments for retirement, an ordinary after tax investment, a tax deferred investment (annuity or IRA), and a Roth IRA. Let an investment earn interest at a steady annual yield r and let your income (what ever year you receive it) be taxed at rate r.
A) Ordinary after-tax investment: Explain why if you earn $ E, pay taxes on it, let what remains earn interest, and pay tax each year on that years interest, the $ E grows after n years to $ E(1-r)x(1+r(1-r)n.
B) Ordinary IRA: Explain why if you earn $ E, defer taxes on it, let what remains earn interest, and defer taxes on all the interest, then the E grows after n years to $ E(1+r)n(1-t).
C) Roth IRA: Explain why if you earn $ E, pay taxes on it, let what remains earn interest, and pay no taxes on all the interest, the $ E grows after n years to $ E (1-r)(1+r)n.
D) Which investment gives the best return after n years?
E) If your marginal tax rate (the rate you pay on one more dollar of income) is lower in one year than the tax rate you expect to pay in retirement, what kind of retirement investment is better for you that year?
If you have a windfall one year and your marginal tax rate is higher that year than the tax rate you expect to pay in retirement, what kind of retirement investment is better for you that year?