Liz begins investing $3,000 once a year in a sinking fund retirement account sta

Question

Liz begins investing $3,000 once a year in a sinking fund retirement account starting at age 22. She stops at age 32, and never invests another penny. It compounds until she is 62. Her brother John starts investing $3,000 in his own account once a year at 32 and continues until he is 62. They both earn 8% interest compounded annually. Who do you think will have more in their retirement account at the age of 62? Support your assertion with calculations or mathematical reasoning. The answer may surprise you! (Hint: Use the future value of a sinking fund for Liz’s 10 years of periodic investments, then the future value of compound interest for the remaining 30 years.)

Explanation / Answer

Liz's Saving:

The at end of 1st year, Liz has = 3000(1+0.08)

The at end of 2nd year, Liz has = [3000(1+0.08) + 3000](1+0.08) = 3000(1.08)^2 + 3000(1.08)

Similary at the end of 10th year Liz has = 3000(1.08)^10 + 3000(1.08)^9 + ... + 3000(1.08) = $46,936.46

Now, this amount will serve as principal for 30 years.

Final amount = 46396.46(1.08)^30 = $ 466,871.66

John's Saving:

The amount that john has at the end of 1st year(age 32) = 3000(1+0.08)

The amount that john has at the end of 2nd year(age 33) = [3000(1+0.08) + 3000](1+0.08) = 3000(1.08)^2 + 3000(1.08)

Similarly amount that John has at the end of 30 years(age 62) = 3000(1.08)^30 + 3000(1.08)^29 + ... + 3000(1.08)

= $367,037.60

Thus, Liz will have more retirement account at the end of age 62

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