Molly's bank pays 10% compound interest on savings annually. Molly dep

Molly pays in compound interest at 10% rate.

Amount = Principal * ( 1+Rate/100)^Time

Amount in the beginning of 1st year = 10,000
For this time = 3 years
Rate =10%
Amount = 10,000(110/100)^3
= 13310

Amount invested in the beginning of second year = 10,000
Time for this =2 years
Rate = 10%
Amount = 10,000(110/100)^2
=12100

Amount invested in the beginning of the 3rd year = 10,000
Time = 1 year
Rate = 10%
Amount = 10,000(110/100)^1
=11000

Total amount he received at the end of 3 years = 13310 + 12100 + 11000 = 36410

IMO D

Molly's bank pays 10% compound interest on savings annually. Molly deposited $10,000 in her account at the start of last year, another $10,000 at the start of this year, and plans to deposit $10,000 more at the start of next year. If she makes no other deposits to or withdrawals from the account, what will be her balance at the end of next year?

A compound Interest question can be solved by Amount formula or by using concept of successive percentage increase or by using year wise break up analysis.

Lets try the Approach 3: Year wise break up

Molly deposited $10,000 in her account at the start of last year. We need to find the compound interest from this deposit after 3 years.

C.I (Compound interest ) in 1 st year = 10 % of 10,000 = 1000
C.I in 2nd year = 10 % of 10,000 + 10 % (First year interest) = 1000 + 10 % of 1000 = 1000 + 100
CI in 3 rd year = 10 % of 10,000 + 10 % (Total interest gained till the end of 2nd year) = 1000 + 10 % of (1000+ 1100) = 1000 + 210

Total CI at the end of 3 years = 1000 + 1100 + 1210 = 3310

We can conclude that Molly will get by default 10 % of 10,000 every year plus some interest from interest.i.e 3* 1000 + interest from interest

Also she made another $10,000 at the start of this year.
The C I from this deposit at the end of 2 years will be 2 * ( 10 % of 10,000) + interest from interest = 2000 + Interest from Interest

or if you want to get the exact value of CI:
C.I in 1 st year = 10 % of 10,000 = 1000
C.I in 2nd year = 10 % of 10,000 + 10 % (First year interest) = 1000 + 10 % of 1000 = 1000 + 100
Total CI in 2 years = 2100

She plans to deposit $10,000 more at the start of next year.
So the CI from this deposit at the end of year = 10 % 10,000 = 1000.

From this, we can conclude that total interest from all the deposits will be 3000 + 2000+1000 + interest from interest = 6000+ interest from interest
Interest from interest will be small compared to interest i.e. 10 % of 10,000

Here in this question, we don't need to spend time finding exact value of CI, a rough estimate we made above is enough to eliminate the options and to reach out to the right answer.

A. $28,075
B. $29,500
C. $33,100
D. $36,410
E. $39,720

Option A and B can be blindly eliminated as the deposits itself will amount to 30,000

Option C can be eliminated as we know that the total interest is slightly more 6000$

Option E can also be eliminated as total interest will never be close to 9000$

Option D is the right answer

Thanks,
Clifin J Francis,
GMAT SME

In total, at the end of next year, Molly will leave her money at the bank: 3 years
Money she will receive for the first-year amount: Principle(1+ rate/1)^3 = 10,000 (1+0.1)^3 = 10,000 * 1.1^3
Money she will receive for the second-year amount: Principle(1+ rate/1)^3 = 10,000 (1+0.1)^2 = 10,000 * 1.1^2
Money she will receive for the third-year amount: Principle(1+ rate/1)^3 = 10,000 (1+0.1)^1 = 10,000 * 1.1^1

==> total money she will receive: 10.000(1.1^3 + 1.1^2 +1.1) = 10.000*(1.331 + 1.21 + 1.1)=
10,000 * 3.641 = 36,410

==> IMO: D