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Sagot :
EXPLANATION
Given that Gloria's Bank Account earned $2,400 in 5 years, we can assevere the following relationship for Simple Interest:
[tex]Amount=P\cdot(1+r\cdot t)[/tex]Where P=Principal r=rate=0.05 t=time=5 years
As the Amount is the sum of the Earns plus the Principal, we can replace the terms as follows:
[tex]\text{Earn}+\text{P}=\text{P}\cdot(1+r\cdot t)[/tex]Subtracting P to both sides:
[tex]\text{Earn}=P\cdot(1+r\cdot t)-P[/tex]Taking P as a common factor:
[tex]\text{Earn}=P\cdot(1+rt-1)[/tex]Dividing both sides by rt:
[tex]\frac{Earn}{rt}=P[/tex]Switching sides:
[tex]P=\frac{Earn}{rt}[/tex]Replacing terms:
[tex]P=\frac{2,400}{0.05\cdot5}[/tex]Simplifying:
[tex]P=\frac{2,400}{0.05\cdot5}=9,600[/tex]In conclusion, the amount deposited was $9,600
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