Question

Find the time required for an investment to double in value if invested in an account paying 3% compounded quarterly.

Answer 1

Answer:
`6.12\ \text{years}`

Explanation:

Given

Rate of interest is
`r=3\%` compounded quarterly

So, annually it is
`r=12\%`

Suppose
`P` is the Principal and A is the amount after certain time period.

Amount in Compound interest is given by

`\Rightarrow A=P[1+r\%]^t`

for given conditions

`\Rightarrow 2P=P[1+0.12]^t\\\Rightarrow 2=(1.12)^t\\\\\Rightarrow t=(\ln (2))/(\ln (1.12))\\\\\Rightarrow t=6.116\approx 6.12\ \text{years}`

It take
`6.12\ \text{years}` to double the invested amount.