Math

posted by Emily

Cliff has some money he wants to invest for his retirement. He is offered two options:
1. 10%/a simple interest
2. 5%/a compounded annually
Under what conditions should he choose the first option?

  1. Damon

    one dollar for n number of years
    1 + .1 n = simple interest earned +1 dollar
    1.05^n = value with compound interest
    when is 1 + .1 n = 1.05^n ?

    1 year 1.1 and 1.05
    2 years 1.2 and 1.10
    3 years 1.3 and 1.16
    4 years 1.4 and 1.22
    .
    .
    .
    10 years 2.0 and 1.62
    .
    .
    .
    20 years 3.0 and 2.65
    .
    .
    .
    25 years 3.5 and 3.38
    .
    .
    .
    30 years 4.0 and 4.32

    So it takes over 25 years for the 5% compounded to be more than the 10% simple. However they will diverge speedily after that.

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