Question

1.) Mark is trying to save up for his retirement at an early age. He decides to deposit $8,000

into a savings account that is compounded continuously. His account has an interest rate
of 5.6%. How many years will it take for Mark's account to reach $30,000?

Answer 1

We can use the formula for continuous compounding:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal amount (initial deposit), e is the constant 2.71828 (from natural logarithms), r is the interest rate as a decimal, and t is the time in years.

We want to solve for t when the amount in the account is $30,000:

30,000 = 8,000e^(0.056t)

Divide both sides by 8,000:

3.75 = e^(0.056t)

Take the natural logarithm of both sides:

ln(3.75) = 0.056t

Solve for t by dividing both sides by 0.056:

t = ln(3.75) / 0.056 ≈ 20.1 years

Therefore, it will take Mark approximately 20.1 years for his account to reach $30,000.