Question

Jermaine invests $5,988 in an account that earns 6.7% that is compounded on a continuous basis. If leaves that money in the account for 9 years, what will be the amount of INTEREST that Jermaine was able to earn? [YOU ARE ASKED TO FIND THE INTEREST ONLY!]

Answer 1

$4955.63

Step-by-step explanation:

When an amount Po is invested and compounded on a continuous basis for a period of t years, we use the formula below to find the amount P(t) after t years.

`P(t)=P_0e^(rt)`

Therefore, the interest that will be earned will be:

`\begin{gathered} Interest=P(t)-P_0=P_0e^(rt)-P_0 \\ =P_0(e^(rt)-1) \end{gathered}`

Substituting the values:

• Po=$5,988

,

• r=6.7%=0.067

,

• t=9 years

We have:

`\begin{gathered} \text{Interest}=5988(e^(0.067*9)-1) \\ =\$4955.63 \end{gathered}`

The amount of INTEREST that Jermaine was able to earn is $4955.63.