Question

Keegan makes a deposit into her savings account at the beginning of the year. The account earns 3% simple interest each year. She has $360.50 in her account at the end of the year. If Keegan did not make any additional deposits or withdrawals during the year, how much did she deposit into the account at the beginning of the year?

Answer 1

Let us assume that she deposited $P in the beginning.
Now it says that account earns simple interest at a rate of 3%.
And after 1 year the balance in account is $360.50.
It means
Amount ,A=$360.50
Rate ,r=3%=0.03
Time,t=1 year
Principal =$P
So Simple Interest earned in 1 year = Amount-principal
We subtract principal from the amount
So
Simple Interest = A-P = 360.50 - P

Now we have a formula for Simple Interest
SI =P*R*T

Lets plug the values
360.50-P = P *0.03*1
360.50-P = 0.03P
Add P to both sides

360.50-P+P =0.03P+P
360.50 = 1.03P

Divide both sides by 1.03
350=P

So we get P=$350
So
Principal =$350
In the beginning she deposited $350

Answer 2

Y= 360.5(1+0.03)^1
y= 360.5(1.03)^1
y= 360.5(1.03)
y= 371.315
y= 371.32