Question

How long would it take for money to double at 11% interest compounded quarterly?

Answer 1

Answer: Approximately 6.3876 years

When rounding to the nearest whole number, this rounds up to 7 years.

===============================================================

Work Shown:

We'll use the compound interest formula

A = P*(1+r/n)^(n*t)

where,

• A = amount of money after t years
• P = initial deposit amount or principal
• r = interest rate in decimal form
• n = compounding frequency
• t = number of years

In this case, we know that,

• A = 2P, since we want the initial amount to double. P can be any positive real number you want and it doesn't affect the answer.
• r = 0.11
• n = 4, since we're compounding 4 times a year
• t = unknown, what we want to solve for

So,

A = P*(1+r/n)^(n*t)

2P = P*(1+r/n)^(n*t)

2 = (1+r/n)^(n*t)

2 = (1+0.11/4)^(4*t)

2 = 1.0275^(4t)

Ln(2) = Ln(1.0275^(4t))

Ln(2) = 4t*Ln(1.0275)

4t*Ln(1.0275) = Ln(2)

t = Ln(2)/(4*Ln(1.0275))

t = 6.38758965414661

It takes roughly 6.3876 years for the deposit to double. If you need this to the nearest whole number, then round up to 7. We don't round to 6 because then we would come up short of the goal of doubling the deposit.