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Difficulty:   15% (low)

Question Stats: 82% (02:02) correct 18% (02:30) wrong based on 534 sessions

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: On a certain day, Tim invested $1,000 at 10 percent annual interest [#permalink] ### Show Tags 1 12 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

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7
6
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.
##### General Discussion
Manager  Joined: 29 Jan 2011
Posts: 235

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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 Manager  Joined: 11 Apr 2011 Posts: 236 Re: On a certain day, Tim invested$1,000 at 10 percent annual interest  [#permalink]

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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 semi-annually, it would mean your amount is being interested once every six months.
Intern  Joined: 01 Jan 2013
Posts: 48
Location: India
Re: On a certain day, Tim invested $1,000 at 10 percent annual interest [#permalink] ### Show Tags 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: 26

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3
1
1
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
SVP  Joined: 06 Sep 2013
Posts: 1521
Concentration: Finance

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tim :

1st year = 1000+ 10% of 1000 = 1100
2nd year : 1100+ 10% 1100 = 1210

interest earned = 1210-1000 = 210

lana : 1st year = 2000+15% of 2000 = 2100
2nd year = 2100+ 15% of 2100 = 2205

interest earned = 2205-2000 = 205

so ans is 210-205 = 5
Non-Human User Joined: 09 Sep 2013
Posts: 14016
Re: On a certain day, Tim invested $1,000 at 10 percent annual interest [#permalink] ### Show Tags 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. _________________ Re: On a certain day, Tim invested$1,000 at 10 percent annual interest   [#permalink] 09 Oct 2019, 06:03
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