Jane and Joan are twins. They both went to work at age 25 with similar jobs, and

Question

Jane and Joan are twins. They both went to work at age 25 with similar jobs, and at the end of each year they will be receiving bonuses of $2000. But there was one (BIG?) difference: Jane is concerned about her future, and plans to invest her $2000 bonus each year in a retirement savings program until age 35, and then have some fun in life by spending the remaining bonuses on Caribbean vacations until she retires at 65. Joan, on the other hand, is convinced she should take opportunities to enjoy life and not be too concerned about saving for the future early on. For the first ten years she plans to spend her $2000 bonuses on vacations in the Bahamas. At age 35, she will start saving for her future and from that time on she will invest her $2000 bonuses until she retires at 65 Each sister is proud of her well-thought-out plan, but who will have more??? Your Job: Investigate what happens to each sister's money over time assuming a long term annual rate of 7%. Write a report to the sisters instructing them on the best plan, be sure to point out who invested more and who had more money at retirement.

Explanation / Answer

In Jane Case:

Future value of annuity = P * ((1+r)^n - 1)/r

where P = $2000

r = 7%

n = 10 years

Value at the end of 35 year = 2000 * (1.07^10 - 1)/.07 = $27632.9

value at the end of 65 year = 1.07^30 * 27632.9 = $201348.65

In Joan Case

value at the end of 65 year = 2000 * (1.07^30 - 1)/.07 = $188921.57

Report:

While analyzing the future value of both the investment made by Jane and Joan one can say that Jane will have more money during her retirement.

Money invested by jane = $2000 * 10 = $20000

Money invested by Joan = $2000 * 30 = $60000

So Joan invested more and Jane accumulated more money during retirement. It happens because Jane started saving early and the money keep growing even after she stopped investing in her reitrement fund. But Joan started late so whe was not able to get the benefit of compunding for more period.

Both sister should follow the Jane method so that they can have more money during retirement.

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