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

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On a certain day, Tim invested $1,000 at 10 percent annual  [#permalink]

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New post 21 Jul 2011, 03:23
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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  [#permalink]

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New post 27 Oct 2013, 05:58
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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?


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Re: Tim invested $1,000  [#permalink]

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New post 21 Jul 2011, 03:50
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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  [#permalink]

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New post 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  [#permalink]

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New post 21 Jul 2011, 05:40
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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.

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Re: Tim invested $1,000  [#permalink]

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New post 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 semi-annually, 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  [#permalink]

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New post 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  [#permalink]

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New post 27 Oct 2013, 16:09
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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  [#permalink]

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New post 28 Oct 2013, 02:19
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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  [#permalink]

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New post 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
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Re: On a certain day, Tim invested $1,000 at 10 percent annual  [#permalink]

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New post 12 Jan 2015, 06:26
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
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Re: On a certain day, Tim invested $1,000 at 10 percent annual  [#permalink]

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New post 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  [#permalink]

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