QUESTION 1 (10 MARKS) You want to save money to meet two objectives. First, you would...

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QUESTION 1 (10 MARKS) You want to save money to meet two objectives. First, you would like to be able to retire 35 years from now with a retirement income of $250,000 per year for 25 years starting at the end of the 36 years from now. And you would like to purchase a cabin in the mountains 10 years from now at an estimated cost of $80,000. You can afford to save only $14,000 per year at the end of each year for the first 20 years. You expect to earn 7.55 percent per year from investments. Assuming you saves the same amount at the end of each year, determine the amount must you save annually from years 21 to 35 to meet your objectives. QUESTION 2 (10 MARKS) Snow Corporation wishes to accumulate funds to provide a retirement annuity for its Vice President of Research, Ms White. Ms White by contract will retire at the end of exactly 12 years. On retirement, she is entitled to receive an annual end- of-year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12-year 'accumulation period', Snow Corporation wishes to fund the annuity by making equal annual end-of- year deposits into an account earning 5.32 percent interest. Once the 20-year 'distribution period' begins, Snow Corporation plans to move the accumulated monies into an account earning a guaranteed 7.13 percent per year. At the end of the distribution period the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13. (a) How large must Snow Corporation's equal annual end-of- year deposits into the account be over the 12-year accumulation period to fund fully Ms White's retirement annuity? (b) How much would Snow Corporation have to deposit annually during the accumulation period if Ms White's retirement annuity was perpetuity and all other terms were the same as initially described? [10 marks] QUESTION 3 (10 MARKS) Consider five investment plans at annual interest rates of 4.85% compounded monthly Investor A: Invest $320 per year for the first 10 years of his career. At the end of 10 years, make no further investments, but reinvest the amount accumulated at the end of 10 years for the next 30 years. Investor B: Do nothing for the first 10 years. Then start investing $320 per year for the next 30 years. Investor C: Invest $320 per year for the entire 40 years. Investor D: Invest $320 per year for the first 5 years, then stop for five years, continue again five years subsequently. After that, make no further investments, but reinvest the amount accumulated at the end of 15 years for the next 25 years. Investor E: Put a lump sum of $5,000 now and start investing $320 per year after the 15 years. Note that all investments are made at the end of each year; the first deposit will be made at n = 1, and you want to calculate the balance at n = 40. QUESTION 1 (10 MARKS) You want to save money to meet two objectives. First, you would like to be able to retire 35 years from now with a retirement income of $250,000 per year for 25 years starting at the end of the 36 years from now. And you would like to purchase a cabin in the mountains 10 years from now at an estimated cost of $80,000. You can afford to save only $14,000 per year at the end of each year for the first 20 years. You expect to earn 7.55 percent per year from investments. Assuming you saves the same amount at the end of each year, determine the amount must you save annually from years 21 to 35 to meet your objectives. QUESTION 2 (10 MARKS) Snow Corporation wishes to accumulate funds to provide a retirement annuity for its Vice President of Research, Ms White. Ms White by contract will retire at the end of exactly 12 years. On retirement, she is entitled to receive an annual end- of-year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12-year 'accumulation period', Snow Corporation wishes to fund the annuity by making equal annual end-of- year deposits into an account earning 5.32 percent interest. Once the 20-year 'distribution period' begins, Snow Corporation plans to move the accumulated monies into an account earning a guaranteed 7.13 percent per year. At the end of the distribution period the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13. (a) How large must Snow Corporation's equal annual end-of- year deposits into the account be over the 12-year accumulation period to fund fully Ms White's retirement annuity? (b) How much would Snow Corporation have to deposit annually during the accumulation period if Ms White's retirement annuity was perpetuity and all other terms were the same as initially described? [10 marks] QUESTION 3 (10 MARKS) Consider five investment plans at annual interest rates of 4.85% compounded monthly Investor A: Invest $320 per year for the first 10 years of his career. At the end of 10 years, make no further investments, but reinvest the amount accumulated at the end of 10 years for the next 30 years. Investor B: Do nothing for the first 10 years. Then start investing $320 per year for the next 30 years. Investor C: Invest $320 per year for the entire 40 years. Investor D: Invest $320 per year for the first 5 years, then stop for five years, continue again five years subsequently. After that, make no further investments, but reinvest the amount accumulated at the end of 15 years for the next 25 years. Investor E: Put a lump sum of $5,000 now and start investing $320 per year after the 15 years. Note that all investments are made at the end of each year; the first deposit will be made at n = 1, and you want to calculate the balance at n = 40.