Question

An investor puts $803.00 in an account that pays 4.00% APR with continuous compounding. What is the future value of this investment in five years?

Answer 1

To calculate the future value of an investment with continuous compounding, you can use the formula:

\[
FV = P \times e^{rt}
\]

where:
- \(FV\) is the future value,
- \(P\) is the principal amount (initial investment),
- \(r\) is the annual interest rate (as a decimal),
- \(t\) is the time in years,
- \(e\) is the base of the natural logarithm (approximately equal to 2.71828).

In this case, you have:
- \(P = 803.00\)
- \(r = 4.00\% = 0.04\)
- \(t = 5\) years

Now you can plug these values into the formula:

\[
FV = 803.00 \times e^{(0.04 \times 5)}
\]

First, calculate \(0.04 \times 5\):

\[
0.04 \times 5 = 0.20
\]

Now calculate \(e^{0.20}\):

\[
e^{0.20} \approx 1.2214
\]

Now calculate the future value:

\[
FV = 803.00 \times 1.2214 \approx 980.44
\]

Therefore, the future value of the investment in five years is approximately **$980.44**.