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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

I have one question based on the following question:

Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4

20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.

I have one question based on the following question:

Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4

20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.

I have one question based on the following question:

Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4

20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.

I have one question based on the following question:

Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4

20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.

You are considering this question in complete vacuum and as such not helping yourself in understanding the nuances involved.

You can also look at it this way: for any period >1 , compound interest > simple interest (or CI is JUST greater than SI) for the same rate.

Rate of interest for quarterly compounding = 12/3 = 3%

Number of quarters in 2 years = 8

Thus SI for this= 20000*3*8/100 = 4800 ---> balance after 2 years = 20000+4800=24800 and hence the final answer will be just greater than 24800. Now in GMAT PS, if the options given to you are spread far apart, then this approximation will give you the correct answer.

But if not, then use the binomial theorem to calculate \((1.03)^8\): \((1.03)^8 = (1+0.03)^8 = 1^8*(0.03)^0+8*1^7*(0.03)^1+28*1^6*(0.03)^2\).... (this last term and the following terms will have 0.03 in 0.03^3 and higher powers making these terms very small compared with others, so neglect them).

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