There are two investment options, Plan A and Plan B, which one would take the least amount of time to double money?

Question

You want to double your money in one year. There are two investment options, Plan A or Plan B. In Plan A, money is compounded continuously for a year at a rate of 4%. In Plan B, money is compounded annually at a rate of 4.3%. Which investment plan will take the least amount of time? And, by how many days?

Answer 1

Plan A: P = initial amount. You double your money when 2P = Pe^0.04t.

So, 2 = e^0.04t. t = ln2 / 0.04 = 17.32868 years = 6325 days

Plan B: 2P = P(1 + 0.043)^t.

2 = (1.043)^t

ln2 = t(ln1.043)

t = ln2 / (ln1.043)= 16.463844 years = 6009.3 days

Answer 2

4% continuously compounded has doubling time = t where

2 = e^.04t take natural logs of both sides

ln2 = .04t

t= ln2/.04 = 25ln2= about 17.33 years

2nd plan 4.3% compounded annually

2 = (1.043)^t take logs to the base 1.043 of both sides

t = log2 to the base 1.043 = ln2/ln1.043 = about 16.46 years

2nd beats 1st by about 17.33 - 16.46 = 0.87 years= 318 days