Question

Looking for the simplest written answers with formulas and a very simple explanation of what you did.

Millhouse graduated 5 years ago with a degree in business administration and is currently employed as a middle level manager for the same firecracker company his dad already worked for. His current annual salary of $60,000 has increased at an average rate of 5% per year and is projected to increase at that rate for the future. The firm has had a voluntary retirement savings program in place, whereby, employees can contribute up to 11% of their gross annual salary (up to a maximum of $11,000 per year) and the company will match every dollar that the employee contributes. Unfortunately, Millhouse did not listen to his finance instructor (which is understandable, because you can't really trust those Germans) and has not yet taken advantage of the retirement savings program. He opted instead to buy a new car, rent an expensive apartment and go out to Moe's every night. However, with wedding plans on the horizon, Millhouse has finally come to the realization (with the help of his fiancée Lisa) that he had better start putting away some money.

Millhouse figures that the two largest expenses down the road would be those related to the wedding and down payment on a house. He estimates that the wedding, which will take place in twelve months, should cost about $10,000. Furthermore, he plans to move into a $200,000 house in 5 years and would need 20% for a down payment. Millhouse knows that an automatic payroll deduction is probably the best way to go since he is not a very disciplined investor.

1) Had Millhouse availed of the company's voluntary retirement plan up to the maximum every year for the past five years, how much money would he currently have accumulated in his retirement account, assuming monthly deposits and a rate of return of 6% with interest compounded monthly? How much more would he have, had he opted for a higher risk alternative which was expected to yield 10%, compounded monthly?

2) If Millhouse starts his retirement savings plan in January of next year (when he turns 28) by contributing the maximum allowable amount into the firm's retirement savings program, how much money will he have accumulated for retirement, assuming he retires at age 65 (27 years later)? Assume the rate of return on the account to be 8% compounded monthly

Answer 1

Problem 1 Calculating the salary drawn each year Year 1 2 4 5 49362.15 51830.26 54421.77 57142.86 60000.00 Employee contribution 5429.84 6285.71 11% 5701.33 5986.39 6600.00 Employer contribution 5701.33 11% 5429.84 5986.39 6285.71 6600.00 Total savings in pension fund 10859.67 904.97 11402.66 11972.79 12571.43 13200.00 950.22 1100.00 1047.62 monthly deposit 997.73 Based on given instructions Millhouse saves every month and hence by applying monthly compounding at 6 % pa we get the following solution Since the problem is monthly compounding, We are going to use 60 months for calculation of the savings Casel: Investing at 6 % perannum compounded monthly Year1 Rate of interest per mont 0.50% Year 2 Year 3 Year 4 Year 5 Accumulated saving: Months Accumulated savings Months Accumulated saving: Months Accumulated saving: Months Accumulated savings 24688.99 Months 38569.23 1 904.97 1 12169.39 1 1 1 53923.45 13180.45 25810.17 39809.70 1814.47 2 2. 2 2 55293.07 31 14196.58 26936.95 41056.37 2728.52 3 56669.53 3 A 4 3647.13 4 15217.78 4 28069.37 4 42309.27 4. 58052.88 4570.34 5 16244.09 29207.45 43568.43 59443.14 6 5498.16 6 17275.53 6 30351.22 6 44833.89 6 60840.36 7 6430.63 7 18312.13 7 31500.71 7 46105.68 7 62244.56 32655.94 33816.96 7367.75 8 19353.91 8 8 47383.83 63655.78 8 8309.56 20400,91 48668.37 9 9 9 9 65074.06 49959.33 51256.74 21453,13 34983.77 10 9256.08 10 10 10 10 66499.43 10207.34 36156.42 67931.93 11 11 22510.62 11 11 11 52560.65 69371.59 12 11163.35 12. 23573.39 12 37334.94 12 12. Total accumulated savings at presnet if millhouse had invested from beginning would be Rs 69371.59

Case 2: Investing at 10 % per annum compounded monthly Year 2 Rate of interest per mont 0.83% Yearl Year 3 Year 4 Year 5 Months Months Accumulated saving: Months Accumulated saving: Months Accumulated savings 25703.19 Accumulated saving: Months Accumulated savings 58485.69 904.97 1817.48 40980.25 1 12416.23 1 1 1 13469.88 26915.03 42369.24 60072.87 2. 2 2 21 2 3 2737.60 3 14532.30 3 28136.96 43769.79 61673.28 63287.02 4 3665.37 15603.58 4 29369.08 4 45182.01 4. 5 4600.88 5 16683.78 30611.45 5 46606.00 5 64914.20 17772.98 6 5544.18 6 6 31864.18 6 48041.84 6 66554.94 7 6495.33 7 18871.25 7 33127.34 71 49489.65 7 68209.34 69877.52 8 7454.41 8 19978.67 8 34401.02 8 50949.52 8 21095.31 71559.60 9 8421.48 9 9 35685.32 9 52421.55 9 22221.25 10 9396.60 10 10 36980.31 10 53905.84 10 73255.69 38286.09 55402.49 74965.91 11 10379.85 11. 23356.58 11 11 11 76690.38 12 11371.29 12 24501.36 12 39602.74 12 56911.62 12 Total accumulated savings at present if millhouse had invested from beginning would be Rs 76690.38 Difference in saving 7318.79

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