I am planning on investing for retirement. I estimate that I will need $100,000

Question

I am planning on investing for retirement. I estimate that I will need $100,000 per year for twenty years. I expect to earn 6%while accumulating and 4% in retirement. . I am now 25 expecting to retire at 67 and have nothing in the plan yet, and from this year I will be contributing equal annual amount. (a) How big must those contributions be? (b) I started on that plan ten years ago and am now 35 and have $80,000 in the plan. If I continue to make the contributions from part (a), what retirement income can I expect? SHOW WORK

Explanation / Answer

a. Value of the retirement income of 100,000 for 20 years at time of retirement = 100,000 * (1-1/(1+4%)^20) / 4% = 1,359,032.63

There are 67-25 = 42 years left till retirement, so 42 annual amounts need to be saved.

Let this annual amount be X.

Then 1,359,032.63 = X * ((1+6%)^42-1) / 6%

Solving, we get X = annual saving amount = 7,723.95

Answer: Annual saving amount = $ 7,723.95

b. There are 67-35 = 32 years left. So 32 equal amounts need to be saved.

Future value of the stream of 32 amounts = 7,723.95 * (((1+6%)^32-1) / 6% = 702,027.80

Future value of the 80,000 already saved = 80,000 * (1+6%)^32 = 516,270.93

Total future value at the time of retirement = 702,027.80 + 516,270.93 = 1,218,298.74

Let the retirement income every year be Y.

Then 1,218,298.74 = Y * (1-1/(1+4%)^20) / 4%

Solving, we get Y = annual retirement income = 89,644.55

Answer: Annual retirement income = $ 89,644.55

Hope this helped ! Let me know in case of any queries.

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