Question

. Find the value of $1,300 invested at 4.2% interest compounded continuously for 5 years, 9 months. Round your final answer to the nearest hundredth, or cent, and show your work. Use e=2.718

Answer 1

The formula we use for continuous compounding is $A=Pe ^{rt}$ where P is the initial amount invested, r is the rate as a decimal, and t is time in years.  Our P = 1300, our r = .042, and our t = 5.75 (9 months is 3/4 of a year, and 3/4 in a decimal is .75).  Putting all that into our formula we have $A=1300(2.718) ^{(.042)(5.75)}$.  We have to multiply those 2 powers together and then raise euler's number to it, then multiply by 1300.  Doing all of that, we get the amount at the end to be $1,655.10