December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST. December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 29 Jan 2011
Posts: 289

On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
21 Jul 2011, 02:23
Question Stats:
81% (02:00) correct 19% (02:27) wrong based on 645 sessions
HideShow timer Statistics
On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? A. $5 B. $15 C. $50 D. $100 E. $105 My Doubts : 1)What does the statement : 10 percent annual interest, compounded annually mean? Does compounded annually mean 5% for first 6 months and 5% for next 6 months ??
2)Can someone solve this using detailed approach?
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51073

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
27 Oct 2013, 04:58
siddhans wrote: On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years? A. $5 B. $15 C. $50 D. $100 E. $105 My Doubts : 1)What does the statement : 10 percent annual interest, compounded annually mean? Does compounded annually mean 5% for first 6 months and 5% for next 6 months ??
2)Can someone solve this using detailed approach? Similar questions to practice: johndeposited10000toopenanewsavingsaccountthat135825.htmlonthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlmichelledepositedacertainsumofmoneyinasavings138273.htmlleonaboughta1year10000certificateofdepositthat143742.htmllouietakesoutathreemonthloanof1000thelender101506.htmlifmoneyisinvestedatrpercentinterestcompoundedannual104225.htmlaninvestmentof1000wasmadeinacertainaccountandear142993.html10000isdepositedinacertainaccountthatpaysr65464.htmllucyboughta1year10000certificateofdepositthatpaid97614.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 11 Apr 2011
Posts: 254

Re: Tim invested $1,000
[#permalink]
Show Tags
21 Jul 2011, 02:50
There are two types of interest rates that GMAT handles with. 1) Simple interest 2) Compound Interest simple interest is basically when you simply multiply your investment amount * interest rate * number of years. Compound interest formula is \(Interest Earned = A * (1+i)^n  A\), where A is your investment amount. The difference between the two can be conveyed with the following example: Suppose you invest 5000 dollars in a bank with an interest rate of 10% for 3 years. Compounded Annually: After 1 year, your bank total would be: [$5000 * 0.10] + $5,000 = $5,500. (Total interest earned = $5,500  $5000 = $500) After 2 years, your bank total would be:[ $5,500 * 0.10] + $5,000 = $6,050. (Total interest earned = $6,050  $5000 = $1050) After 3 years, your bank total would be: [ $6,050 * 0.10] + $5,000 = $6655. (Total interest earned = $6,655  $5000 = $1,655) * Using the compounded interest formula above will give you the same answer.* Whereas, simple interest for the same investment would be: After 1 year, your bank total would be: $5,000 * 0.10 * (1) + $5,000 = $5,500. (Total interest earned = $5,500  $5000 = $500) After 2 years, your bank total would be: [$5,000 * 0.10 * 2] +$5,000 = $6,000. (Total interest earned = $6,000  $5000 = $1000) After 3 years, your bank total would be: [$5,000 * 0.10 * 3] + $5,000 = $6,500 (Total interest earned = $6,500  $5000 = $1,500) As you can see, "Compounded annually" charges interest on the bank balance which includes both the initial investment amount + the cumulative interest earned from that investment whereas simple interest is based solely on the interest earned from just the initial investment amount.
_________________
Powerscore CR Bible Full Chapter Notes  Easily Extend Vocabulary List with Google Dictionary
Please kudo me if you found my post useful. Thanks!!!




Senior Manager
Joined: 29 Jan 2011
Posts: 289

Re: Tim invested $1,000
[#permalink]
Show Tags
21 Jul 2011, 04:19
Mahtab wrote: There are two types of interest rates that GMAT handles with. 1) Simple interest 2) Compound Interest
simple interest is basically when you simply multiply your investment amount * interest rate * number of years.
Compound interest formula is \(Interest Earned = A * (1+i)^n  A\), where A is your investment amount.
The difference between the two can be conveyed with the following example: Suppose you invest 5000 dollars in a bank with an interest rate of 10% for 3 years.
Compounded Annually: After 1 year, your bank total would be: [$5000 * 0.10] + $5,000 = $5,500. (Total interest earned = $5,500  $5000 = $500) After 2 years, your bank total would be:[$5,500 * 0.10] + $5,000 = $6,050. (Total interest earned = $6,050  $5000 = $1050) After 3 years, your bank total would be: [$6,050 * 0.10] + $5,000 = $6655. (Total interest earned = $6,655  $5000 = $1,655)
*Using the compounded interest formula above will give you the same answer.*
Whereas, simple interest for the same investment would be: After 1 year, your bank total would be: $5,000 * 0.10 * (1) + $5,000 = $5,500. (Total interest earned = $5,500  $5000 = $500) After 2 years, your bank total would be: [$5,000 * 0.10 * 2] +$5,000 = $6,000. (Total interest earned = $6,000  $5000 = $1000) After 3 years, your bank total would be: [$5,000 * 0.10 * 3] + $5,000 = $6,500 (Total interest earned = $6,500  $5000 = $1,500)
As you can see, "Compounded annually" charges interest on the bank balance which includes both the initial investment amount + the cumulative interest earned from that investment whereas simple interest is based solely on the interest earned from just the initial investment amount. What does the term compounded annually mean ? interest received twice in a year? i.e once every 6 months ?



Intern
Joined: 18 Jul 2011
Posts: 43

Re: Tim invested $1,000
[#permalink]
Show Tags
21 Jul 2011, 04:40
Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly  in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have 1,000(1.10)^2 = 1,000(1.21) = 1,210 and Lana would have 2,000(1.05)^2 = 2,000(1.1025) = 2,205 Thus, Tim earned 210 dollars, while Lana earned 205 dollars The difference is $5 and the answer is A.
BenchPrepGURU



Senior Manager
Joined: 11 Apr 2011
Posts: 254

Re: Tim invested $1,000
[#permalink]
Show Tags
11 Mar 2012, 10:38
siddhans wrote: What does the term compounded annually mean ? interest received twice in a year? i.e once every 6 months ?
Compounded annually means your bank amount is being interested once per year (yearly). If it was semiannually, it would mean your amount is being interested once every six months.
_________________
Powerscore CR Bible Full Chapter Notes  Easily Extend Vocabulary List with Google Dictionary
Please kudo me if you found my post useful. Thanks!!!



Manager
Joined: 01 Jan 2013
Posts: 51
Location: India

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
27 Oct 2013, 03:29
siddhans wrote: On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
A. $5 B. $15 C. $50 D. $100 E. $105
My Doubts : 1)What does the statement : 10 percent annual interest, compounded annually mean? Does compounded annually mean 5% for first 6 months and 5% for next 6 months ??
2)Can someone solve this using detailed approach? calculate simple interest for both lana and tim Tim interest = 20% X 1000 = 200+ Additional interest due to compounding Lana interest= 10%x2000 = 200+ additional interest due to compouding but the difference between two compounded interest would be very less Hence Ans A) Had the option was 7$ as well ,then calculation would be required here.



Intern
Joined: 17 Dec 2012
Posts: 29

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
27 Oct 2013, 15:09
After first year both person would have an interest of 100 (10 % of 1000 = 100 & 5 % of 2000 is 100)
The interest for next year is also 100 for both person as above
The difference in the net interest is between the interest added to both account.
Therefore for the account with 10 % interest the additional interest is 10 % of 100 = 10
and for the other account it is 5% of 100 = 5
Hence net difference = 10 5 = 5



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
28 Oct 2013, 01:19
Tim: Int for 1st Yr =100 Int for 2nd Yr = 110 (compounded) Lana: Int for 1st Yr =100 Int for 2nd Yr = 105 (compounded) Difference: = 100 + 110  (100 + 105) =5
_________________
Kindly press "+1 Kudos" to appreciate



SVP
Joined: 06 Sep 2013
Posts: 1728
Concentration: Finance

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
04 Feb 2014, 07:32
irda wrote: After first year both person would have an interest of 100 (10 % of 1000 = 100 & 5 % of 2000 is 100)
The interest for next year is also 100 for both person as above
The difference in the net interest is between the interest added to both account.
Therefore for the account with 10 % interest the additional interest is 10 % of 100 = 10
and for the other account it is 5% of 100 = 5
Hence net difference = 10 5 = 5 I agree one should notice that after the first year interest is the same, they both earn 100 bucks Now, in second year Tim gains 1100/10 = 110 Lana gains 2100*5/10 = 105 So difference is 5 A is the correct answer Hope it helps Cheers J



Intern
Joined: 23 Dec 2014
Posts: 47

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
12 Jan 2015, 05:26
tim :
1st year = 1000+ 10% of 1000 = 1100 2nd year : 1100+ 10% 1100 = 1210
interest earned = 12101000 = 210
lana : 1st year = 2000+15% of 2000 = 2100 2nd year = 2100+ 15% of 2100 = 2205
interest earned = 22052000 = 205
so ans is 210205 = 5



Intern
Joined: 09 Mar 2017
Posts: 49
Location: India
GPA: 4
WE: Marketing (Advertising and PR)

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
15 Jul 2017, 03:00
It took me 3 and a half minute to solve this! Even with a lot of practice, such questions tend to take a lot of time cause of calculations.



NonHuman User
Joined: 09 Sep 2013
Posts: 9102

Re: On a certain day, Tim invested $1,000 at 10 percent annual
[#permalink]
Show Tags
04 Aug 2018, 10:03
Hello from the GMAT Club BumpBot! 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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: On a certain day, Tim invested $1,000 at 10 percent annual &nbs
[#permalink]
04 Aug 2018, 10:03






