GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Calculating Compound Interest

Jessica deposits $5,000 in a savings account at 6% interest. The interest is compounded monthly. How much will she have in her savings account after 5 years?

Possible Answers:

$\$6500$

$\$6744$

$\$2744$

$\$1500$

None of the other answers are correct.

Correct answer:

$\$6744$

Explanation:

$A=P(1+\frac{r}{n})^{nt}$

where is the principal, is the number of times per year interest is compounded, is the time in years, and is the interest rate.

$A=5000(1+\frac{0.06}{12})^{(12)(5)}=6744$

Report an Error

Example Question #1 : Calculating Compound Interest

A real estate company is considering whether to accept a loan offer in order to develop property. The principal amount of the loan is $400,000, and the annual interest rate is 7% compounded semi-anually. If the company accepts the loan, what will be the balance after 4 years?

Possible Answers:

615,130

414,000

491,720

526,720

14,000

Correct answer:

526,720

Explanation:

Recall the formula for compound interest:

$Amount=P(1+r/n)^{nt}$ , where n is the number of periods per year, r is the annual interest rate, and t is the number of years.

Plug in the values given in the question:

$400,000(1+0.07/2)^{2\cdot 4}=400,000(1.035)^{8}=$

400,000(1.3168)=526,720

Report an Error

Example Question #2 : Calculating Compound Interest

Nick found a once-in-a-lifetime opportunity to buy a rare arcade game being sold at a garage sale for $5730. However, Nick can't afford that right now, and decides to take out a loan for $1000. Nick didn't really read the fine print on the loan, and later figures out that the loan has a 30% annualy compounded interest rate! (A very dangerous rate). How much does Nick owe on the loan 2 years from the time he takes out the loan? (Assume he's lazy and doesn't pay anything back over those 2 years.)

Possible Answers:

$\$3000$

$\$1690$

$\$1600$

$\$5070$

$\$152.10$

Correct answer:

$\$1690$

Explanation:

For compound interest, the amount Nick owes is

P(1+i)^t

where is the principal, or starting amount of the loan ($1000), is the interest rate per year (30% = .3). and is the time that has passed since Nick took out the loan. (2)

We have

1000(1+.3)^2 =1000(1.3)^2 = 1000(1.3)(1.3)=1000(1.69)=1690

Hence our answer is $1690.

Report an Error

Example Question #21 : Interest Problems

Casey deposits $\$1000$ in his savings account that pays $10\%$ interest compunded yearly. Two years later, he deposits $\$100$ more into the same saving account. How much money is in Casey's account three years after he started his account?

Possible Answers:

$\$1400$

$\$1441$

$\$1500$

$\$1464.10$

$\$1844.10$

Correct answer:

$\$1441$

Explanation:

We will make use of the formula A = P(1+i)^t where is the accumulated amount, is the starting amount, is the rate of interest, and is the time in year the money is invested.

At the beginning, Casey starts with $1000, at an interest rate of 10% (or .1) and saves his money for 2 years. So after 2 years, he has

1000(1+.1)^2 = 1000(1.1)^2 = 1000(1.21) = 1210 dollars in his account.

After he sees the $1210, he deposits $100 more, and then waits one more year.

Now becomes 1310. And after this 3rd year, Casey has

1310(1.1)^1 = 1441 in his account.

Report an Error

Example Question #11 : Calculating Compound Interest

If you invest $\$10,000$ today into a fund which earns a $10\%$ annually compounded interest, what amount of money will you have in the fund years from now?

Possible Answers:

$\$13,310$

$\$12,100$

$\$14,520$

$\$14,461$

$\$13,000$

Correct answer:

$\$13,310$

Explanation:

The accumulated amount at the end of 3 years will be $10,000 x (1.1)^3 .

It is easier to find the correct answer by using the following approach:

Calculate the amount accumulated at the end of each year. (Note that the interest is compounded, so use the amount accumulated at the end of the previous year to calculate the interest for the next year.)

At the end of year 1

$Amount\:accumulated= 10000 x (1+0.1) = 10000+1000=11,000$

At the end of year 2

$Amount\:accumulated= 11000 x (1+0.1) = 11000+1100=12,100$

At the end of year 3

$Amount\:accumulated= 12100 x (1+0.1) = 12100+1210=13,310$

Report an Error

Example Question #31 : Interest Problems

$\$45,000$ is invested at $6\%$ compounded annual interest rate, how much will the investment yield after one year?

Possible Answers:

$\$4,254$

$\$2,700$

$\$3,250$

$\$5,400$

$\$1,350$

Correct answer:

$\$2,700$

Explanation:

This problem simply ask for the amount of interest received one year after having invested this money. We could, for this problem, either use the simple interest formula or the compounded interest formula, which is $P\left(1+\frac{r}{c}\right)^{n\cdot c}-P$ , where is the principal, the rate, the number of compounding periods and the number of years for which we invest. We substract because we only want the amount of interest, not the total value at the end of periods. Note that is positive for increases and negative for decreases.

Applying this formula we get,

$45,000\left(1+\frac{0.06}{1}\right)^{1\cdot 1}-45,000$ , giving us 2700 .

Report an Error

Example Question #11 : Calculating Compound Interest

$\$45,000$ is deposited in an account paying $6\%$ compounded annual interest rate, how much will there be on the account after two years?

Possible Answers:

$\$51,789$

$\$50,100$

$\$47,700$

$\$50,562$

$\$50,132$

Correct answer:

$\$50,562$

Explanation:

We apply the compound interest rate formula

A=P(1+r)^t

where P=principal, r=rate, and t=time.

Pluggin in our values we get

$45,000(1+0.06)^{2}$ , or 50,562 .

Report an Error

Example Question #31 : Interest Problems

We invest $\$100,000$ for two years in an investment paying interest rates. At the end of the two years we end up with $\$132,250$ . What is ?

Possible Answers:

$12\%$

$15\%$

$14\%$

$11\%$

$13\%$

Correct answer:

$15\%$

Explanation:

The way we should treat this problem is as an equation and plug in what we know in the compounded interest formula, as follows: $100,000(1+r)^{2}=132,250$ . By manipulating the terms we get: $(1+r)^{2}= 1.3225$ . Now, since it would be too complicated to solve this quadratic equation, we should just try with the values in the answers. For example let's try with the square of 1.12 , which turns out to be 1.2544 , therefore it is too small and we should look for a larger rate. Let's try until we find the right answer. Remember when you test answers to find the right answer, make sure you go slow so you don't have to test twice in case you would make an error.

Report an Error

Example Question #14 : Calculating Compound Interest

Ten years ago today, Geri's grandmother deposited some money into a college fund that yielded interest at a rate of 3.6% compounded monthly. There is now $6,400 in the account. Assuming that no money has been deposited or withdrawn, which of the following expressions must be evaluated in order to determine the amount of money originally deposited?

Possible Answers:

$6,400 e ^{0.36}$

$6,400 - 6,400 \cdot 0.036 \cdot 10$

$\frac{6,400}{\left $1 .003 \right $^{12 0}}$

$6,400 \cdot 1 .003 ^{12 0}$

$\frac{6,400 }{e ^{0.36}}$

Correct answer:

$\frac{6,400}{\left $1 .003 \right $^{12 0}}$

Explanation:

The formula for compound interest is

$A = P \left $1+ \frac{r}{n} \right $^{nt}$ ,

where is the current, or accrued, value of the investment, is the initial amount invested, or principal, is the annual rate expressed as a decimal, is the number of periods per year, and is the number of years.

In this scenario,

A = 6,400 , r=0.036, n = 12, t = 10 ,

so the equation becomes

$6,400 = P \left $1+ \frac{0.036}{12} \right $^{12 \cdot 10}$

$6,400 = P \left $1+0.003 \right $^{12 0}$

$6,400 = P \left $1 .003 \right $^{12 0}$

$P = \frac{6,400}{\left $1 .003 \right $^{12 0}}$

Report an Error

Example Question #15 : Calculating Compound Interest

Veronica's aunt invested $4,000 in some corporate bonds for her niece the day Veronica was born; the bonds paid 4% annual interest compounded continuously. No money was deposited or withdrawn over the next eighteen years.

Which of the following expressions is equal to the amount of money in the account on Veronica's eighteenth birthday?

Possible Answers:

$\frac{4,000 }{e^{0.72}}$

$\frac{4,000 }{e^{1.72}}$

$4,000 e^{0.72}$

4,000 (1 .72)

$4,000 e^{1.72}$

Correct answer:

$4,000 e^{0.72}$

Explanation:

The formula for continuously compounded interest is

$A = P e^{rt}$

where is the current, or accrued, value of the investment, is the initial amount invested, or principal, is the annual rate expressed as a decimal, and is the number of years.

In this scenario,

P = 4,000 , r=0.04 , t = 18 ,

$A = 4,000 e^{0.04 \cdot 18} = 4,000 e^{0.72}$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in San Francisco-Bay Area, Physics Tutors in Miami, SSAT Tutors in Los Angeles, Computer Science Tutors in Atlanta, ISEE Tutors in Dallas Fort Worth, Physics Tutors in Phoenix, Calculus Tutors in San Francisco-Bay Area, Math Tutors in Los Angeles, Chemistry Tutors in San Francisco-Bay Area, MCAT Tutors in San Diego

Popular Courses & Classes

Spanish Courses & Classes in San Diego, GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Boston, LSAT Courses & Classes in Denver, MCAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Boston, GRE Courses & Classes in Boston, ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Denver, LSAT Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in Boston, GMAT Test Prep in New York City, MCAT Test Prep in Denver, LSAT Test Prep in Denver, SSAT Test Prep in Seattle, SAT Test Prep in New York City, LSAT Test Prep in San Diego, LSAT Test Prep in Houston, GMAT Test Prep in San Diego, GRE Test Prep in San Francisco-Bay Area

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating Compound Interest

Example Question #1 : Calculating Compound Interest

Example Question #2 : Calculating Compound Interest

Example Question #21 : Interest Problems

Example Question #11 : Calculating Compound Interest

Example Question #31 : Interest Problems

Example Question #11 : Calculating Compound Interest

Example Question #31 : Interest Problems

Example Question #14 : Calculating Compound Interest

Example Question #15 : Calculating Compound Interest

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details