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 = 6238.3 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