Question

christian is going to invest $9,400 and leave it in an account for 18 years. assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for christian to end up with $15,300?

Answer 1

Using the continuous compounding interest formula, the interest rate necessary for Christian's investment to grow from $9,400 to $15,300 over 18 years is approximately 2.7%.

Step-by-step explanation:

Christian is looking to determine the necessary interest rate needed for his investment to grow from $9,400 to $15,300 over 18 years with continuous compounding. To solve this, we use the formula for continuous compounding interest, A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested for in years.

First, let's isolate the interest rate (r) in the formula:

A = Pert

$15,300 = $9,400ert

$15,300 / $9,400 = ert

ln($15,300 / $9,400) = rt
r = ln($15,300 / $9,400) / t
Using this formula, let's plug in the values:

r = ln($15,300 / $9,400) / 18
r ≈ ln(1.62766) / 18
r ≈ 0.4836 / 18
r ≈ 0.02687
To convert this to a percentage, we multiply by 100:

r ≈ 2.687%

The interest rate, rounded to the nearest tenth of a percent, is 2.7%.