Paragraph Styles FIN 101 Homework #17 Please write (type) your answers to the qu
ID: 2790559 • Letter: P
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Paragraph Styles FIN 101 Homework #17 Please write (type) your answers to the questions here, then save and submit them as A woman is in the 25% marginal tax bracket, and is considering the tax consequences of investing $2000 at the end of the year for 30 years in a tax-sheltered retirement account, assuming that the investment earns 8% annually. A) How much will her account total over 30 years if the growth in the investment 1) remains sheltered from taxes? B) How much will the account total if the investments are not sheltered from taxes? Use Appendix A-3 for both A and B A married couple desire an annual retirement income of $40,000. They expect to live for 30 years past retirement. Assuming that the couple could earn a 3% after-tax and after-inflation rate of return on their investments, what amount of accumulated savings and investments would they need? Use Appendix A-4 2)Explanation / Answer
FV of annuity The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows: P = PMT x ((((1 + r) ^ n) - 1) / i) Where: P = the future value of an annuity stream PMT = the dollar amount of each annuity payment r = the effective interest rate (also known as the discount rate) i=nominal Interest rate n = the number of periods in which payments will be made If the returns are sheltered from Taxes Accumulation =2000* ((((1 + 8%) ^ 30) - 1) / 8%) Accumulation 226,566 If the returns are not sheltered from Taxes return available =8%*(1-25%) 6.00% Accumulation =2000* ((((1 + 6%) ^ 30) - 1) / 6%) Accumulation 158,116 Solution 2 Desired annual retirement income is 40000 PV of such retirment income @ 3% for 30 years will be the balance which couple should have PV of annuity for making pthly payment P = PMT x (((1-(1 + r) ^- n)) / i) Where: P = the present value of an annuity stream PMT = the dollar amount of each annuity payment r = the effective interest rate (also known as the discount rate) i=nominal Interest rate n = the number of periods in which payments will be made =40000*(((1-(1 + 3%) ^-30)) /3%) 784,018 So they should have 784,018 in their account to finance their retirement time
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