Question

Tyler invested $350 in an account paying an interest rate of 4.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $700 ?

Answer 1

It would take approximately 15.4 years for Tyler's $350 investment to reach $700 at a 4.5% continuous compounding interest rate.

Step-by-step explanation:

When calculating how long it will take for an account with compounded continuously interest to double, we use the natural exponential function. The formula for continuous compounding is A = Pe^{rt}, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), and t is the time in years.

In Tyler's case, he wants his initial investment of $350 (P) to grow to $700 (A), with an interest rate of 4.5% or 0.045 (r). We will solve for t using natural logarithms:

• $700 = $350e^{0.045t}
• 2 = e^{0.045t}
• ln(2) = 0.045t
• t = ln(2) / 0.045
• t ≈ 15.4 years

To the nearest tenth of a year, it would take Tyler approximately 15.4 years for his investment to reach $700.