Question

Jocelyn is going to invest $610 and leave it in an account for 12 years. Assuming theinterest is compounded continuously, what interest rate, to the nearest tenth of apercent, would be required in order for Jocelyn to end up with $1,220?

Answer 1

0.06 or 6% as a percentage.

Explanation:

We have that the related formula in this case is the following:

`\begin{gathered} A=P\cdot(1+r)^t \\ A\text{ = Amount} \\ P\text{ = Principal} \\ r\text{ = interest rate} \\ t\text{ = time} \end{gathered}`

Replacing each value and solving for r

`\begin{gathered} 1220=610\cdot(1+r)^(12) \\ (1+r)^(12)=(1220)/(610) \\ (1+r)^(12)=2 \\ 1+r=\pm\sqrt[12]{2} \\ r=\pm\sqrt[12]{2}-1 \\ r_1=0.06 \\ r_2=-2.06 \end{gathered}`

Since the interest cannot be negative, the correct interest is 0.06 or 6% as a percentage.