s. Carrie Mathison plans to retire in 30 years. She intends to contribute the sa

Question

s. Carrie Mathison plans to retire in 30 years. She intends to contribute the same amount of money each year to her retirement fund. The fund earns 10% compounded annually. She would like to withdraw $100,000 each year for 20 years, starting one year after the last contribution is made. How much money should she contribute to her fund each year? 6. A new rail car costs $100,000 and is expected to last for twenty years, assuming that $20,000 is spent on a major overhaul at the end of year 10. Routine servicing and maintenance are expected to cost $2,000 per year. The car is expected to be used in revenue service for 300 days per year. What is the equivalent cost per-day-in-use over the twenty-year life of the car, assuming a discount rate of 10%? 7. An industrial firm uses an economic analysis to determine which of two different machines to purchase. Each machine is capable of performing the same task in a given amount of time. Assume the minimum attractive rate of return is 8%. Use the following data in this analysis. Initial cost Estimated life Salvage value Annual maintenance cost $150 Machine x Machine y $6000 S12,000 7 years 13 years none $4000 $175 Which, if either of the two machines should the firm choose based on equivalent uniform annual costs?

Explanation / Answer

Answer to th fifth question

she will be withdrawing $100,000 from the account starting on 31st year to 50th year so, we find the present value of the fund on the 31st year. discounting rate is taken at 10%. Present value = future inflows/((1+r)^n) = [FV1/(1+r)^1]+[FV2/(1+r)^2]+[FV3/(1+r)^3+………[FV(n)/(1+r)^n] where, r= rate of interest or discounting factor n= term Calculating the present value of the fund at 31st year. discounting factor at 31st year = (1/1.1) = 0.909 32nd year = 1/(1.1^2) = 0.8264 . . 50th year = 1/(1.1^20) = 0.1486 Adding up the discounting factors for the 20 years is = 8.5136 therefore present value of the amount withdrawn each year from 31 year to 50th year is = $100,000*8.5136 = $851,360 Therefore to withdraw $100,000/- each year after her retirement for 20 years she should have $851,360/- in her account. To have such amount in account in the year of retirement she contributes same amount of money each year to her retirement fund. let the cash outflow each year be 'x' Formula: f = d[(1 + i)^n - 1] / i f = Future Value = 851360 d = Principal amoount of deposit = x n = time period = 30 I = interest rate = 10% Future value of ordinary annuity: 851360 = x+x*1.1+x*1.1^2+…+5x*1.1^29 851360 = x(1.1^30-1)/(.1) x = 51756/- She should contribute $51,756/- each year for 30 years to retirement fund

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