Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)

Question

Initial	InvestmentAnnual	% RateTime to	DoubleAmount After	10 Years
$850	%
9 1
2	yr	$

Answer 1

continuously compounding formula is

A=Pe^rt where P =starting amount = $850, r=annual interest rate, t= time in years, e=2.718281828...

A = ending amount

to find doubling time, A=2P

and the formula becomes 2P=Pe^rt

or more simply

2=e^rt

take natural logs of both sides to get

ln2=rt

divide by r

t=ln2/r = doubling time,

doubling time is the same regardless of the initial investment so ignore $850 for this calculation

just plug in the interest rate to calculate time t

if r=10% then

t=ln2/.1 = about 6.93 years = about 6 years 11 months

to find A in 10 years

A=850e^10r

if r= 10%= .1 then

A=850e10(.1) = 850e = $2,310.54

use a calculator with a natural log function. Its inverse will be the "e" function

or to really save time, or just to check your answer

go online to a continuous compounding calculator website

such as omnicalculator.com

plug in r, t, P or any 3 of the 4 variables, in A=Pe^rt, and the website will instantly give you the 4th missing variable. (e is not a variable, it's a fixed constant irrational number)

but your chart does say "investment annual" which may mean the $850 is invested annually? or maybe not. Buf If so, it gets a little more complicated with a different formula. and more websites will also do the work for you.