wive las fromint Dorein! be drewet morth it a=0 II - BaP Bristulein diention 1. tf. withdrawals Arealrelate Boestion 1 in 1. You decide to start saving for your retirement. You open a savings account bearing interest 10% p. a. (per annum) with monthly compounding (thus the effective monthly interest rate is 10%+12 =0.8333% ). Over the next 30 years, at the end of each month, you deposit $100 into this account. a. How much money will you have in your account immediately after the last deposit? Continue: One month after depositing the last deposit you start making constant monthly withdrawals to finance your retirement (the first withdrawal occurs exactly one month after the last deposit). b. How much money can you withdraw each month, if you want your funds to last exactly 20 years? c. How long will your funds last, if you withdraw $1,000 each month? If $2,000 ? d. If you want to withdraw $1,000 each month over the next 20 years, how much you need to deposit monthly in years 130 ? e. Think again about task b. Withdrawing equal amount may not be optimal because of inflation: money gradually loses its value. Suppose you expect average inflation to be 3% per year (accrued gradually throughout each year). Recalculate the withdrawal amounts such that your withdrawals have constant purchasing power. (To illustrate: Imagine you consume nothing else but beer. You want to consume 100 bottles per month. Initially beer costs $1 a bottle. Thus, a withdrawal of $100 allows you to consume exactly 100 bottles in the first month. Next month, beer prices increase a bit by the amount of the monthly inflation. Assume that the beer price next month is $1.01 per bottle. Then you need to withdraw $101 to be able to buy 100 bottles. And so on.) f. Think again about task d. Withdrawing equal amount may not be optimal because of inflation: money gradually loses its value. Suppose you expect average inflation to be 3% per year (accrued gradually throughout each year). Find the deposit amount that gives you $1,000 monthly withdrawal at real prices. L.e., the first withdrawal will be $1,000, the next withdrawal will be increased by one-month inflation etc. (Assume the deposit amount is constant and is not adjusted for inflation.) 2. (adding taxes) Assume the income tax is 30%, and the interest is taxable when earned. Recalculate Question 1. d. 3. (switching from savings account to investment account; tax on realized vs. unrealized gain) Assume that your deposits are made into a securities investment account 1 instead, earning constant 10% return per annum, with monthly compounding. The return is earned only in the form of unrealized capital gains (i.e., the increase in value of securities held, with no dividends or similar cash distributions received), and hence is not immediately taxable 2. One month after the last deposit you sell your securities, pay the tax on the realized capital gain, move your funds to more conservative assets paying a fixed interest rate of 3% per year with monthly compounding (thus the interest is taxable immediately when earned), and, at the same moment, start making constant monthly withdrawals. Recalculate Question 1.d. 1) Investment account does not hold cash, but securities such as bonds, stocks, or derivatives. 2) The unrealized capital gain (loss) is the profit (loss) that you would make if you sold the securities; the realized capital gain is the profit that you make if and when you sell the securities.) In many tax legislations, the unrealized capital gain is not taxable, the realized capital gain is. wive las fromint Dorein! be drewet morth it a=0 II - BaP Bristulein diention 1. tf. withdrawals Arealrelate Boestion 1 in 1. You decide to start saving for your retirement. You open a savings account bearing interest 10% p. a. (per annum) with monthly compounding (thus the effective monthly interest rate is 10%+12 =0.8333% ). Over the next 30 years, at the end of each month, you deposit $100 into this account. a. How much money will you have in your account immediately after the last deposit? Continue: One month after depositing the last deposit you start making constant monthly withdrawals to finance your retirement (the first withdrawal occurs exactly one month after the last deposit). b. How much money can you withdraw each month, if you want your funds to last exactly 20 years? c. How long will your funds last, if you withdraw $1,000 each month? If $2,000 ? d. If you want to withdraw $1,000 each month over the next 20 years, how much you need to deposit monthly in years 130 ? e. Think again about task b. Withdrawing equal amount may not be optimal because of inflation: money gradually loses its value. Suppose you expect average inflation to be 3% per year (accrued gradually throughout each year). Recalculate the withdrawal amounts such that your withdrawals have constant purchasing power. (To illustrate: Imagine you consume nothing else but beer. You want to consume 100 bottles per month. Initially beer costs $1 a bottle. Thus, a withdrawal of $100 allows you to consume exactly 100 bottles in the first month. Next month, beer prices increase a bit by the amount of the monthly inflation. Assume that the beer price next month is $1.01 per bottle. Then you need to withdraw $101 to be able to buy 100 bottles. And so on.) f. Think again about task d. Withdrawing equal amount may not be optimal because of inflation: money gradually loses its value. Suppose you expect average inflation to be 3% per year (accrued gradually throughout each year). Find the deposit amount that gives you $1,000 monthly withdrawal at real prices. L.e., the first withdrawal will be $1,000, the next withdrawal will be increased by one-month inflation etc. (Assume the deposit amount is constant and is not adjusted for inflation.) 2. (adding taxes) Assume the income tax is 30%, and the interest is taxable when earned. Recalculate Question 1. d. 3. (switching from savings account to investment account; tax on realized vs. unrealized gain) Assume that your deposits are made into a securities investment account 1 instead, earning constant 10% return per annum, with monthly compounding. The return is earned only in the form of unrealized capital gains (i.e., the increase in value of securities held, with no dividends or similar cash distributions received), and hence is not immediately taxable 2. One month after the last deposit you sell your securities, pay the tax on the realized capital gain, move your funds to more conservative assets paying a fixed interest rate of 3% per year with monthly compounding (thus the interest is taxable immediately when earned), and, at the same moment, start making constant monthly withdrawals. Recalculate Question 1.d. 1) Investment account does not hold cash, but securities such as bonds, stocks, or derivatives. 2) The unrealized capital gain (loss) is the profit (loss) that you would make if you sold the securities; the realized capital gain is the profit that you make if and when you sell the securities.) In many tax legislations, the unrealized capital gain is not taxable, the realized capital gain is