You are currently 30 years old. You intend to retire at age 60, and you want to

Question

You are currently 30 years old. You intend to retire at age 60, and you want to be able to receive a 20-year, $100,000 beginning-of-the-year annuity, with the first payment to be received on your 60th birthday. You would like to save enough money over the next 15 years to achieve your objective; that is, you want to accumulate the necessary funds by your 45th birthday.

If you expect your investments to earn 12% per year over the next 15 years and 10% per year thereafter, how much must you accumulate by the time you reach age 45?

What equal, annual amount must you save at the end of each of the next 15 years to achieve your objective, assuming you currently have $10,000 available to meet your goal? Assume the conditions stated in section A.

Explanation / Answer

Answer

present value required at 60th birthday to receive $100000 for 20 years = 851356.37

present value at 45 years = 851356/(1+0.1)^15 = 203808

Amount required to invest per year from 30 - 45:

Fv = (Pv(1+r)^n - 1)/r

203808 = (Pv(1+0.12)^15 - 1)/0.12

Amount Required to invest per year = $5467

Present value of amount recd between 60-80 year Particulars Time PV Amount PV Cash Flows 1 0.9091       100,000      90,909.09 Cash Flows 2 0.8264       100,000      82,644.63 Cash Flows 3 0.7513       100,000      75,131.48 Cash Flows 4 0.6830       100,000      68,301.35 Cash Flows 5 0.6209       100,000      62,092.13 Cash Flows 6 0.5645       100,000      56,447.39 Cash Flows 7 0.5132       100,000      51,315.81 Cash Flows 8 0.4665       100,000      46,650.74 Cash Flows 9 0.4241       100,000      42,409.76 Cash Flows 10 0.3855       100,000      38,554.33 Cash Flows 11 0.3505       100,000      35,049.39 Cash Flows 12 0.3186       100,000      31,863.08 Cash Flows 13 0.2897       100,000      28,966.44 Cash Flows 14 0.2633       100,000      26,333.13 Cash Flows 15 0.2394       100,000      23,939.20 Cash Flows 16 0.2176       100,000      21,762.91 Cash Flows 17 0.1978       100,000      19,784.47 Cash Flows 18 0.1799       100,000      17,985.88 Cash Flows 19 0.1635       100,000      16,350.80 Cash Flows 20 0.1486       100,000      14,864.36 TOTAL    851,356.37

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