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 interestAlso 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 interestInterest 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 answerThanks,
Clifin J Francis,
GMAT SME _________________