Question

William invested $550 in an account paying an interest rate of 2% compounded monthly. Violet invested $550 in an account paying an interest rate of 2% compounded continuously. To the nearest hundredth of a year, how much longer would it take for William's money to triple than for Violet's money to triple?​

Answer 1

We can use the formula A = P(1 + r/n)^(nt) to find out how long it takes for William's money to triple, where A is the final amount, P is the principal, r is the interest rate, t is the time in years and n is the number of times the interest is compounded per year.

A = P(1 + r/n)^(nt) = 550(1 + 0.02/12)^(12*t) = 3P

Solving for t we get

t = (ln(3)/ln(1+0.02/12))/12 = 49.41

For Violet's account, using the formula A=Pe^(rt) where A is the final amount, P is the principal, r is the interest rate, t is the time in years, we get:

t = ln(3) / (2 * e^-2) = 49.41

Therefore, it will take approximately 49.41 years for William's money to triple, and 49.41 years for Violet's money to triple.

So the difference in time is 0.