Question #65796

2 Answers
Oct 4, 2017

#6.35# years

Explanation:

#A=P(1+(r/100))^n#
where
A = Amount, P = Principal, r = annual rate of interest & n = no. of years.
Given A = 2P after n years.
#:.2P=P(1+(11.55/100))^n#
#2=(1.1155)^n#
Taking log on both sides,
#log2=n*log(1.1155)#
#n=log(2)/log(1.1155)#
#n=0.3010/0.0474=6.35# years

Oct 6, 2017

See below

Explanation:

We could use the formula given in the problem description:

#FV=PVe^(rt)#

The questions is asking for time, so let's make #t# the subject:

#e^(rt)=(FV)/(PV)#

Let's take the natural log of both sides to cancel out the exponential:

#rt=ln((FV)/(PV))#

We are looking for how long it will take for the money to double. So, that means: FV = 2(PV). If we substitute #FV# above and solve for #t#, the equation becomes:

#ln(2)/r=ln(2)/0.1155=6 years#

Good Paper about PV and FV of Continuous Income Streams