Question

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?

Answer 1

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.