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.
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