GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Jun 2018, 14:35

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

### Show Tags

07 Dec 2012, 03:29
3
29
00:00

Difficulty:

15% (low)

Question Stats:

74% (01:06) correct 26% (01:22) wrong based on 2092 sessions

### HideShow timer Statistics

Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? (A)$10,464
(B) $864 (C)$ 816
(D) $800 (E)$ 480
Math Expert
Joined: 02 Sep 2009
Posts: 46264
Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 07 Dec 2012, 03:35 13 17 Walkabout wrote: Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 Approach #1: 8 percent compounded semiannually --> 4% in 6 moths. For the first 6 moths interest was 4% of$10,000, so $400; For the next 6 moths interest was 4% of$10,000, plus 4% earned on previous interest of $400, so$400+$16=$416;

Total interest for 1 year was $400+$416=$816. Answer: C. Approach #2: If the interest were compounded annually instead of semiannually then in a year the interest would be 8% of$10,000, so $800. Now, since the interest is compounded semiannually then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than$800, only answer choice C fits.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html
michelle-deposited-a-certain-sum-of-money-in-a-savings-138273.html

Theory:
math-number-theory-percents-91708.html

Hope it helps.
_________________
Manager
Joined: 11 Aug 2012
Posts: 124
Schools: HBS '16, Stanford '16

### Show Tags

10 Jun 2013, 05:09
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Percent and Interest Problems: math-number-theory-percents-91708.html

All DS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=33
All PS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=54

_________________
Intern
Joined: 09 Apr 2013
Posts: 40
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 750 Q50 V41
GPA: 3.55
WE: General Management (Non-Profit and Government)

### Show Tags

26 Jun 2013, 00:32
4
2
This problem can be solved using formula. However, the calculation in formula is difficult = 10,000(208/200)^2.

The main motive of GMAT behind Compound interest problem is to consume your time so that you waste your precious time in difficult calculations. We have to avoid that trap and use simple and fast calculations.

By definition Compound interest = S.I. + Interest on Interest

So here C.I. = 4% on 10,000 (6months) + 4% on 10,000(6months) + 4% on interest (last 6 months interest)

= 400 + 400 + 4*400/100
= 400 + 400 + 16 = 816
_________________

Thanks & Regards
Yodee

‘A good plan violently executed now is better than a
perfect plan executed next week.’

- General Georg S. Patton

Intern
Joined: 19 Jan 2014
Posts: 26
Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 25 May 2014, 16:47 Walkabout wrote: Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 I did it this way. I find it to be easy way for compound interest questions so maybe it will help someone. annual interest 8%. semiannual = 4% (8/2) how many times 4%? 2 times 10 000x104/100x104/100=104x104=10 816 10 816-10 000=816 Intern Affiliations: ScoreBoost Joined: 07 Sep 2012 Posts: 14 Location: India Re: Leona bought a 1-year,$10,000 certificate of deposit that [#permalink]

### Show Tags

27 May 2014, 03:18
4
The amount increases in two steps : 4% in the first 6 months and again 4% in the second 6 months.

Such % change in two steps is knows as successive % change.

In case of successive % change, we can use the below formula to calculate the Net % change :

$$Net % change =$$ $$A + B + \frac{AB}{100}$$

If there is % increase , we take the value as positive and for % decrease, we take that as negative.

In the final answer, positive number shows % increase and negative number shows % decrease.

Using the above formula , we get : net change = $$4 + 4 + \frac{4*4}{100}$$ $$= 8 + .16 = 8.16 %$$.

$$8.16 % of 10,000$$ is 816. Hence the answer is 816.

This formula is applicable only in case of % change in two steps. In case % change takes place in 3 steps, we have to apply the formula for the first two first and then to the result and the third one.
_________________

Quant Instructor
ScoreBoost
Bangalore, India

Intern
Joined: 11 Nov 2014
Posts: 12
GMAT Date: 01-15-2015
GPA: 3.4

### Show Tags

14 Apr 2015, 08:43
Is this approach correct?

Interest= (P*R*T)/100

For first 6 months, I = (10000*8*0.5)/100=400
Amount = P + I = 10400

For second 6 months, previous amount becomes the principal
I = (10400*8*0.5)/100= 416

So total interest = 400+416=816
Retired Moderator
Joined: 23 Sep 2015
Posts: 387
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

### Show Tags

07 Jun 2016, 10:55
Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? (A)$10,464
(B) $864 (C)$ 816
(D) $800 (E)$ 480

We use the compound interest equation:

Future Value = (Present Value)(1 + r/n)^nt

where r is the annual interest rate, n is the number of compounding periods per year and t is the amount of time (in years) until maturity.

So we know:

Present Value = 10,000

r = 8% = 0.08

n = 2

t = 1

So we have:

FV = 10,000(1+0.08/2)^(2)(1)

FV = 10,000(1+0.04)^2

FV = 10,000(1.04)(1.04)

FV = 10,000(1.0816) = $10,816 Thus, the amount of interest earned is$10,816 – $10,000 =$816.

We could have also looked at this problem a bit more conceptually. We know that when an investment has a rate of 8% ANNUAL interest and it compounds SEMI-ANNUALLY (twice a year), the investment earns 4% interest every SIX MONTHS. So in this case we know:

Interest earned for the first six months = 0.04 x $10,000 =$400

Her investment is now worth ($400 +$10,000) = $10,400 Interest earned for the next six months = 0.04 x$10,400 = $416 Thus, the total interest earned =$400 + $416 =$816

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 21 Sep 2015
Posts: 80
Location: India
GMAT 1: 730 Q48 V42
GMAT 2: 750 Q50 V41

### Show Tags

12 Jun 2016, 09:00
2
Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? (A)$10,464
(B) $864 (C)$ 816
(D) $800 (E)$ 480

Compound interest= P (1+r/100n)^n

10,000 (1+8/200)^2

10,000 * 104/100 *104/100

Units digit will be 6. Only option C has units digit of 6
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 27 Jun 2017, 08:36 Walkabout wrote: Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 $$A = 10000 ( 1 + \frac{8}{200})^2$$ Or, $$A = 10000*1.04^2$$ Or, $$A = 10816$$ So, Interest paid on this certificate at maturity is$ 816, answer must be (C)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Retired Moderator
Joined: 19 Mar 2014
Posts: 974
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 27 Jun 2017, 12:57 Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

1. Premium for first 6 months: $$10,000 * \frac{8}{100}$$ = $$800$$

As the interest is getting compounded semiannually, new principal will be = $$10,000 +  800$$ = $$10,800$$

2. Premium for next 6 months: $$10,800 * \frac{80}{100}$$= $$816$$

Hence, Total Interest Paid = $$816$$

Hence, the Answer is C
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Director
Joined: 02 Sep 2016
Posts: 744
Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 10 Sep 2017, 02:38 Compound interest formula is the best way to solve this problem. But we can also use the simple interest formula: Amount*Rate*Time/100 = 10000*8*1/100 =800 The answer would be slightly more than 800 i.e. 816. _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Re: Leona bought a 1-year,$10,000 certificate of deposit that   [#permalink] 10 Sep 2017, 02:38
Display posts from previous: Sort by

# Leona bought a 1-year, \$10,000 certificate of deposit that

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.