Question

Question #65796

Answer 1

`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

Answer 2

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