If $5,000 is invested at 4% interest, find the value of the investment (in dollars) at the end of 3 years if the interest is compounded continuously

Answer 1

Hello,

This problem calls for using the continuously compounding interest formula, which is:

X = P * e ^(r*t)

^where

^{X = Future Value **** what you need to find}

^{P = Initial Principal (starting cash)}

^{e = natural exponential function}

^{r = interest rate}

^{t = time}

^{The confusing part here can be found in correctly identifying how to express the correct rate and time.The assumption to be made here given no specific terminology is given is that the 3% interest rate is an ANNUAL RATE (per year). Once you can determine the above mentioned, it's more or less a process to plug in the information you have and find what you don't have.}

X = Solve for this.

r = 0.04 (this is 4% in decimal form)

t = 3 years

P = $5,000

X = 5,000 * e ^{(0.04 * 3)}

X = 5,000*1.1275

^{P = $5637.50}

^{Note: Since this problem involves actual currency as the units of measure, make sure to round the final answer to 2 decimal places, as in the nearest "cent".}