Question

Aubree is going to invest $18,000 and leave it in an account for 5 years. Assuming the

interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Aubree to end up with $19,000?

Answer 1

1.08%

Explanation:

You want to know the continuously compounded interest rate that will result in a value of $19,000 for an investment of $18,000 after 5 years.

Continuous compounding

The value of an investment of P earning continuously compounded interest at rate r for t years is ...

A = Pe^(rt)

Application

Using the given values, we can solve for r:

19000 = 18000·e^(r·5)

19/18 = e^(5r) . . . . . . . . . . . divide by 18000

ln(19/18) = 5r . . . . . . . . . . take natural logs

r = ln(19/18)/5 ≈ 0.0108 = 1.08%

The required interest rate is about 1.08%.

<95141404393>