Question

How long does it take for an investment to double in value if it is invested at 2% compounded quarterly? Compounded continuously?At 2% compounded quarterly, the investment doubles in about(Round to two decimal places as needed)years

Answer 1

The SOLUTION

Recall the formula for compound interest formula

`A=P(1+(r)/(n))^(nt)`

For the amount to double then A=2P

From the question it follows:

`\begin{gathered} r=2\%=0.02 \\ n=4 \end{gathered}`

Substituting these values gives:

`2P=P(1+(0.02)/(4))^(4t)`

Solve for t

`\begin{gathered} 2=1.005^(4t) \\ \Rightarrow t\approx34.74 \end{gathered}`

Therefore the number of years it will take for the amount to double is 34.74 years

Using the compounded continuously formula

Substituting values gives

`2P=Pe^(0.02t)`

Solve for t

`\begin{gathered} 2=e^(0.02t) \\ \Rightarrow t\approx34.66 \end{gathered}`

For compounded continuously, the investment will double in about 34.66 years