Question

If a couple has $80,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 6% compounded continuously? Round to the nearest year.

Answer 1

Using the formula for continuous compounding (A = Pe^rt), it will take approximately 35 years for $80,000 to grow to $1,000,000 at a 6% rate compounded continuously.

Step-by-step explanation:

To calculate how long it will take for $80,000 to grow to $1,000,000 with compound interest compounded continuously at a 6% rate, we use the formula for continuous compounding, which is A = Pert, where A is the future value, P is the principal amount, r is the rate of growth, and t is the time in years.

Rearranging the formula to solve for t, we get t = (ln(A/P)) / r.

Plugging in the values, we have A = $1,000,000, P = $80,000, and r = 0.06.

So, t = (ln(1,000,000/80,000)) / 0.06.

After calculating, we find that it will take approximately 35 years for the money to grow to $1,000,000, rounding to the nearest year.