# If Emery has $1400 to invest at 11% per year compounded monthly, how long will it be before he has $2300. If the compounding is continuous, how long will it be?

Algebra

(a) ##t = 4.52 years## or about 54 months (b)##t=4.5## years

Given: ##P = 1400## ##r=0.11## ##m = 12 ( monthly)## ##A=2300## ##t=?## (no. of years) (a) Formula: ##A=P(1+i)^n## where ##i=r/m## and ##n=mt## Solution: ##2300=1400(1+0.11/12)^(12t)## divide both sides by 1400 ##(2300/1400)= 1.0092^(12t)## get the logarithm of both sides ##log(2300/1400)= log(1.0092)^(12t)## ##0.2156=12t(3.9772×10^-3)## dividing both sides of the equality by ##12(3.9772×10^-3)## gives ##t = 4.52 years## or about 54 months (b) Formula: ##A = Pe^(rt)## ##2300=1400e^(0.11t)## divide both sides by 1400 ##2300/1400=e^(0.11t)## get the natural logarithm of both sides ##ln(2300/1400)=lne^(0.11t)## ##0.49463=0.11t## dividing both sides by 0.11, ##t=4.5## years