Posted by Ana on Tuesday, April 20, 2010 at 5:02am.
Get Rich Quick Investments LTD offers 2 investment schemes.
Scheme 1: Earn 6.5% interest per year, compounded monthly.
Scheme 2: Earn 6.45% interest per year, compounded daily.
An investor reasons that Scheme 2 should be the best because its interest rate is very close to 6.5%, but the compounding occurs daily. Using each scheme, compare how long it would take to double your investment, and hence determine whether the investor is correct.

Maths  Reiny, Tuesday, April 20, 2010 at 7:25am
A simple way to see which is the higher rate is to take an arbitrary amount of money, say $100, and see how much it grows to in one year
Scheme 1: amount = 100(1 + .065/12)^12 = 106.697
Scheme 2: amount = 100(1 + .0645/365)^365 = 106.662
so what do you think?
Let's find the effective annual rate of each
we can get it by dividing our answers above by 100
scheme 1: annual rate = 6.697%
scheme 2 : annual rate = 6.662%
so solving for
2 = 1(1.06697)^n
n = log 2/log 1.06697 = 10.69 years
for scheme 2:
2 = 1(1.06662)^n
n = log2/log 1.06662) = 10.75 years