Question

If a couple has $100,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 8% compounded continuously? Round up to the nearest year.

Answer 1

It will take approximately 11 years for the money to grow to $1,000,000 if it grows by 8% compounded continuously.

Step-by-step explanation:

To find out how long it will take for the money to grow to $1,000,000, we can use the formula for compound interest:

A = P * e^(rt)

Where:

A = the final amount (in this case, $1,000,000)

P = the initial amount (in this case, $100,000)

e = Euler's number (approximately 2.71828)

r = annual interest rate (in this case, 8%)

t = time

Let's substitute the values and solve for t:

$1,000,000 = $100,000 * e^(0.08t)

Divide both sides by $100,000:

10 = e^(0.08t)

Take the natural logarithm of both sides to isolate t:

ln(10) = 0.08t

Divide both sides by 0.08:

t = ln(10)/0.08 ≈ 10.98 years

Rounded up to the nearest year, it will take approximately 11 years for the money to grow to $1,000,000 if it grows by 8% compounded continuously.