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:

• $P=803.00$
• $r=4.00$
• $t=5$ 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.