Jonathan test at $8000 higher ra

Question

Jonathan invested $1000 at a rate of 2.6% compounded continuously. How much will be investment be within five years? How long will it take you to Doublr

Answer 1

When dealing with continuous compounding we use the formula A = Pe^rt (P is your principal or the amount you start with, e is euler's number, r is your interest rate in decimal form, and t is time). For the first part it wants us to find the amount after 5 years:

A = 1000 e^(.026*5) This is fairly easy, just plug it into your calculator.

A = $1,138.83

For the second part, we want to know how long it takes to double so we will be solving for t. To show that our amount doubles we will say our "P" is 1 which would mean our "A" would be 2 since we are doubling our "P":

2 = 1 e^(.026*t)

2 = e^(.026*t) To cancel out the "e" we will multiple both sides by the natural log "ln"

ln2 = ln(e^(.026t)

ln2 = .026t Now we divide both sides by .026

(ln2)/.026 = t Plug into your calculator

26.7 = t

If you have any additional questions don't hesitate to reach out :)