Question

A person places $13900 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.

Answer 1

The Solution:

Given the formula:

`V=Pe^(rt)`

We are required to find the amount in the account after 18 years.

In this case,

`\begin{gathered} V=\text{ ?} \\ P=\text{ \$13900} \\ r=2.8\text{\%}=0.028 \\ t=18\text{ years} \end{gathered}`

Substituting these values in the above formula, we get

`V=13900e^(0.028*18)=23009.078\approx\text{ \$23009.08}`

Therefore, the correct answer is $23009.08