An initial investment of $10,000 was deposited in a bank account one

Given: An initial investment of $10,000 was deposited in a bank account one year ago, and additional deposits were made during the year.

Target question: What was the total amount of interest earned on this account during the year?

Statement 1: The additional deposits during the year totaled $5,000.
Since we have no information about the interest rate, statement 1 is NOT SUFFICIENT

Statement 2: The account earned interest at the annual rate of 6 percent compounded quarterly.
Since we have no information about the additional deposits, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Even when we combine two statements, there is still no way to answer the target question with certainty, since we have no idea WHEN the additional $5000 was deposited.
Better understand why, let's say the original $10,000 was deposited on January 1, 2019
Now consider these two possible cases:

Case a: The additional $5000 was deposited on January 1, 2019.
In this case, 1 year's interest was collected on the original $10,000 AND 1 year's interest was collected on the additional $5000
So, the TOTAL interest = 6% of $15,000


Case b: The additional $5000 was deposited at 11:59 pm on December 31, 2019.
In this case, 1 year's interest was collected on the original $10,000 AND no interest was collected on the additional $5000
So, the TOTAL interest = 6% of $10,000

As we can see, the two different cases yield different values of the TOTAL interest
So, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

principal = 10,000
additional deposits be x (but we still don't know whether these deposits be equal and periodic)
rate be r%
time = 1 year (during the year)
now, we need to find interest earned on the account, lets assume it to be I.

simple formulas regarding compound and simple interest, to know about variables:
I = Amount- Principal
Amount = Principal*(1+[(r/(n*100)))^(n*t)]
if interest rate is compound interest

I = Amount- Principal
Amount = Principal*(1+(r*t))
if rate is simple interest

1. additional deposits total = 5000
not sufficient since we don't know what and how much rate of interest is?

2. Rate of interest = 6% compounded quarterly
ok, we have rate now and its 6% and compounded quarterly

but we don't have the additional deposits and their details.

therefore, A, B, D --> x

we have to find an answer from C, and E.
combining both the information from 1 and 2, we get
additional deposits = 5000
rate= compounded quarterly, 6%
Again, not sufficient as we don't have sufficient information regarding additional deposits, As in how many installments and these installments are periodic or not, and these individual additional deposits are equal or not.

Therefore, E.

Given : 10,000 deposited into the bank and some additional deposits were made during the year.

To find : the interest rate earned during the year

Solution:
Statement 1: 5,000 were deposited additionally. But when? And at what interest rate? (Not sufficient)

Statement 2: account earn interest at the rate of 6% compounded quarterly.
But what about additional deposits? (Not sufficient)

1&2: 5000 is additional deposits and 6% interest rate compounded quarterly.
But when that deposits are made in bank. Early quarterly. Mid quaterly.
We don't know.

So answer has to be E

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