Question

QuestionIn 5 years, Gloria's bank account earned $2,400 interest at 5%. How much had she deposited in the account?

Answer 1

EXPLANATION

Given that Gloria's Bank Account earned $2,400 in 5 years, we can assevere the following relationship for Simple Interest:

`Amount=P\cdot(1+r\cdot t)`

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:

`\text{Earn}+\text{P}=\text{P}\cdot(1+r\cdot t)`

Subtracting P to both sides:

`\text{Earn}=P\cdot(1+r\cdot t)-P`

Taking P as a common factor:

`\text{Earn}=P\cdot(1+rt-1)`

Dividing both sides by rt:

`(Earn)/(rt)=P`

Switching sides:

`P=(Earn)/(rt)`

Replacing terms:

`P=(2,400)/(0.05\cdot5)`

Simplifying:

`P=(2,400)/(0.05\cdot5)=9,600`

In conclusion, the amount deposited was $9,600