Question

Looking for the accumulated value if the money is compounded continuously?

Answer 1

Continuous Compound

An initial investment of P dollars at an interest annual rate r will have a final value A given by:

`A=P\cdot e^(r\cdot t)`

The investment is P = $15,000 at a rate of r = 4.5% = 0.045. The accumulated (or final) value for t = 5 years is:

`\begin{gathered} A=15,000\cdot e^(0.045\cdot5) \\ \text{Calculating:} \\ A=15,000\cdot e^(0.225) \\ A=15,000\cdot1.252323 \\ A=18,784.84 \end{gathered}`

The Accumulated value is $18,784.84