Suppose you start a savings plan in which you save $500 each year for 15 years.

Question

Suppose you start a savings plan in which you save $500 each year for 15 years. You make your first payment at age 22 and then leave the accumulated sum in the savings plan (and make no more annual payments) until you reach age 65, at which time you withdraw the total accumulated amount. The average annual interest rate you'll earn on this savings plan is 10%. A friend of yours (exactly your age) from Minnesota State University waits 10 years to start her savings plan. She decides to save $2,000 each year in an account earning interest at the rate of 10% per year. She will make these annual payments until she is 65 years old, at which time she will withdraw the total accumulated amount. How old will you be when your friend's accumulated savings amount (including interest) exceeds yours? 5.

Explanation / Answer

Answer : At the age of 39 years , as calculated below in detail worksheet.

YOU FRIEND FROM MINNESOTA UNIVERSITY Age Invesment Accumulated Fund Age Invesment Accumulated Fund 22 $500 $550.00 22 $0 $0.0 23 $500 $1,155.00 23 $0 $0.00 24 $500 $1,820.50 24 $0 $0.00 25 $500 $2,552.55 25 $0 $0.00 26 $500 $3,357.81 26 $0 $0.00 27 $500 $4,243.59 27 $0 $0.00 28 $500 $5,217.94 28 $0 $0.00 29 $500 $6,289.74 29 $0 $0.00 30 $500 $7,468.71 30 $0 $0.00 31 $500 $8,765.58 31 $0 $0.00 32 $500 $10,192.14 32 $2,000 $2,200.0 33 $500 $11,761.36 33 $2,000 $4,620.00 34 $500 $13,487.49 34 $2,000 $7,282.00 35 $500 $15,386.24 35 $2,000 $10,210.20 36 $500 $17,474.86 36 $2,000 $13,431.22 37 $0 $19,222.35 37 $2,000 $16,974.34 38 $0 $21,144.59 38 $2,000 $20,871.78 39 $0 $23,259.05 39 $2,000 $25,158.95 40 $0 $25,584.95 40 $2,000 $29,874.85 41 $0 $28,143.44 41 $2,000 $35,062.33 42 $0 $30,957.79 42 $2,000 $40,768.57 43 $0 $34,053.57 43 $2,000 $47,045.42 44 $0 $37,458.92 44 $2,000 $53,949.97 45 $0 $41,204.82 45 $2,000 $61,544.96 46 $0 $45,325.30 46 $2,000 $69,899.46 47 $0 $49,857.83 47 $2,000 $79,089.41 48 $0 $54,843.61 48 $2,000 $89,198.35 49 $0 $60,327.97 49 $2,000 $100,318.18 50 $0 $66,360.77 50 $2,000 $112,550.00 51 $0 $72,996.85 51 $2,000 $126,005.00 52 $0 $80,296.53 52 $2,000 $140,805.50 53 $0 $88,326.19 53 $2,000 $157,086.05 54 $0 $97,158.80 54 $2,000 $174,994.65 55 $0 $106,874.68 55 $2,000 $194,694.12 56 $0 $117,562.15 56 $2,000 $216,363.53 57 $0 $129,318.37 57 $2,000 $240,199.88 58 $0 $142,250.21 58 $2,000 $266,419.87 59 $0 $156,475.23 59 $2,000 $295,261.86 60 $0 $172,122.75 60 $2,000 $326,988.05 61 $0 $189,335.02 61 $2,000 $361,886.85 62 $0 $208,268.53 62 $2,000 $400,275.53 63 $0 $229,095.38 63 $2,000 $442,503.09 64 $0 $252,004.92 64 $2,000 $488,953.40 65 $0 $277,205.41 65 $2,000 $540,048.74

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