Question

How long will it take for $900 to double if it is invested at 11% annual interest compounded 3 times a year?
Enter in exact calculations or round to 3 decimal places.

It will take _____ years to double.

How long will it take if the Interest is compounded continuously?

Compounded continuously, it would only take ____ years.

Answer 1

Answer:

• 3 times per year: 6.416 years
• continuously: 6.301 years

Step-by-step explanation:

You want the doubling time for an investment at 11% annual interest, compounded 3 times per year, and if it were compounded continuously.

Compound interest

For interest compounded n times per year at annual rate r for t years, the multiplier of the investment is ...

  k = (1 +r/n)^(nt)

We want to find t when the multiplier is 2.

  2 = (1 +0.11/3)^(3t)

Taking logarithms, we have ...

  log(2) = 3t·log(1 +0.11/3)

  t = log(2)/(3·log(1 +0.11/3)) ≈ 6.416 . . . . years

It will take 6.416 years to double.

Continuously compounded interest

When the interest is compounded continuously, the multiplier is ...

  k = e^(rt)

Filling in the values of k and r, and taking logarithms, we have ...

  2 = e^(0.11t)

  ln(2) = 0.11t

  ln(2)/0.11 ≈ 6.301 . . . . years

It would only take 6.301 years.