Question

Ingrid deposits $10,000 in an IRA. What will be the value of her investment in 6 years if the investment is earning 3.2% per year and is compounded continuously? Round to the nearest cent.

Answer 1

We have a initial deposit of $10,000 (PV=10,000).

The investment last 6 years (t=6).

The annual interest rate is 3.2% (r=0.032) and is compounded continously.

The equation to calculate the future value FV of the inverstment for this conditions is:

$\begin{gathered} FV=PV\cdot e^{rt} \\ FV=10,000\cdot e^{0.032\cdot6} \\ FV=10,000\cdot e^{0.192}. \\ FV\approx10,000\cdot1.2116705 \\ FV\approx12,116.71 \end{gathered}$

The value of her investment will be $12,116.71.