SOLUTION: i'm doing business algebra online in college, and we're now talking about continuous compound interest. The formula i'm struggling with is the Pert formula. I'm stuck on how to s

Question 256355: i'm doing business algebra online in college, and we're now talking about continuous compound interest. The formula i'm struggling with is the Pert formula. I'm stuck on how to solve a problem when i know what the P, r and t is, but what is the e for? I've never figured out how to come up with the same answer as my study guide example.
For example: Use the continuous compound interest formula to find the indicated value. A=$7,700; r=8.78%; t=10 years; P=? P=_______(round to two decimal places as needed).
I look forward to getting a reply back soon. Hopefully I will get this figured out soon. Thank you.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
with continuous compounding formula, you get:

f = future value
p = present amount
r = annual interest rate
t = number of years

the e is the symbol for the scientific constant of 2.718281828...

This is an irrational number (never ending non repeating fractional part).

It's called Napier's constant.

the formula for the base of e to an exponent is where x is the exponent.

the inverse formula of is equal to which means the natural log of x.

the basis definition of is:

if and only if .

this is nothing more than your normal logarithm functions except you have a base of e.

It's no different than the statement:

if and only if

for example:

let x = 3

{y = 10^3}}} = 10*10*10 = 1000

the statement becomes:

if and only if .

you can confirm that by using your calculator and taking the log of 3.

you will get 1000.

the base e is nothing more than another base to work with.

In your problem, here's how you would work it.

formula is .

you are given:

p = $7,700
r = 8.78%
t = 10 years

first thing you need to do is take all the dollar signs and commas out of p to get:

p = 7700

next thing you need to do is divide 8.78% by 100% to get .0878.

in the formula, you need to work with the rate, not the percent.

since r is an innual interest rate already, you do not need to adjust it any further.

since t is already specified in years, you do not need to adjust it any further.

plug these values into your formula to get:

becomes

simplify to get:

use your calculator to get = 2.406082726

alternatively, you can substitute the constant of 2.718281828 to get:

solve for f to get:

f = 18526.83699

that's equivalent to $18,526.84.

for some good examples of continuous compounding, check out the web.

do a search on "continuous compounding".

one such website is http://moneychimp.com/articles/finworks/continuous_compounding.htm

It has a calculator that lets you calculate different numbers and see the effect of continuous compounding compared to discrete compounding such as yearly, monthly, daily, and hourly.

It also has a box where you can put in the number of time periods you want.

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