Question

In $5$ years, Gloria’s bank account earned $$2400$ interest at $5$%. How much had she deposited in the account?

Short answer

Gloria’s bank account earned $$2400$interest at $5$% in five years then she might have deposited $$9600$ in the account?

Step-by-step solution

Step 1. Given information    

simple interest$I=\$2400$

Interest rate$$\begin{gathered} r=5\% \\ r=0.05 \end{gathered}$$

Time$t=5$

Step 2. Principal  

Consider the principal is P

Substitute simple interest, interest rate, and time in Simple interest formula

$$\begin{gathered} I=Prt \\ 2400=P(0.05)\left(5\right) \\ 2400=0.25P \\ \frac{2400}{0.25}=P \\ P=9600 \end{gathered}$$

So the Principal was $$9600$.

Step 3. Verification   

Simple interest of principal $$9600$ with interest rate $5$% and time $5$years is

$$\begin{gathered} I=Prt \\ I=9600(0.05)\left(5\right) \\ I=2400 \end{gathered}$$

simple interest is $$2400$which is the same as given in the question

so the principal of $$9600$is correct.