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On a certain day, Tim invested $1,000 at 10 percent annual
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21 Jul 2011, 03:23
Question Stats:
81% (01:59) correct 19% (02:28) wrong based on 468 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?
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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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27 Oct 2013, 05:58




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Re: Tim invested $1,000
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21 Jul 2011, 03:50
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.
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Re: Tim invested $1,000
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21 Jul 2011, 05:19
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 ?



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Re: Tim invested $1,000
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21 Jul 2011, 05:40
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.
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Re: Tim invested $1,000
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11 Mar 2012, 11:38
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.
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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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27 Oct 2013, 04:29
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.



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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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27 Oct 2013, 16:09
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



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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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28 Oct 2013, 02:19
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
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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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04 Feb 2014, 08:32
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



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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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12 Jan 2015, 06:26
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



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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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15 Jul 2017, 04:00
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.



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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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Re: On a certain day, Tim invested $1,000 at 10 percent annual
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