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# On a certain day, Tim invested $1,000 at 10 percent annual interest SORT BY: Tags: Show Tags Hide Tags Manager Joined: 29 Jan 2011 Posts: 158 Own Kudos [?]: 723 [58] Given Kudos: 87 Most Helpful Reply Math Expert Joined: 02 Sep 2009 Posts: 94776 Own Kudos [?]: 646242 [19] Given Kudos: 86843 Manager Joined: 11 Apr 2011 Posts: 221 Own Kudos [?]: 1227 [16] Given Kudos: 13 General Discussion Manager Joined: 29 Jan 2011 Posts: 158 Own Kudos [?]: 723 [0] Given Kudos: 87 Re: On a certain day, Tim invested$1,000 at 10 percent annual interest [#permalink]
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: On a certain day, Tim invested $1,000 at 10 percent annual interest [#permalink] 8 Kudos 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: On a certain day, Tim invested $1,000 at 10 percent annual interest [#permalink] 1 Kudos 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: 39 Own Kudos [?]: 121 [1] Given Kudos: 131 Location: India Re: On a certain day, Tim invested$1,000 at 10 percent annual interest [#permalink]
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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?

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: 21 Own Kudos [?]: 68 [5] Given Kudos: 34 Re: On a certain day, Tim invested$1,000 at 10 percent annual interest [#permalink]
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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 interest [#permalink] 5 Kudos 3 Bookmarks 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 VP Joined: 06 Sep 2013 Posts: 1335 Own Kudos [?]: 2457 [0] Given Kudos: 355 Concentration: Finance Re: On a certain day, Tim invested$1,000 at 10 percent annual interest [#permalink]
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 interest [#permalink] 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 Intern Joined: 02 Nov 2020 Posts: 26 Own Kudos [?]: 7 [0] Given Kudos: 1 Re: On a certain day, Tim invested$1,000 at 10 percent annual interest [#permalink]
Here's an explanation on YouTube. (This GMAT question, by the way, is a great introduction to questions about compound interest.)

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Re: On a certain day, Tim invested $1,000 at 10 percent annual interest [#permalink] Can someone solve this and explain? What is a fast way to solve the multiplier raised to an exponent ? (1.1^3 & 1.05^3) Thank you Non-Human User Joined: 09 Sep 2013 Posts: 34223 Own Kudos [?]: 857 [0] Given Kudos: 0 Re: On a certain day, Tim invested$1,000 at 10 percent annual interest [#permalink]
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Re: On a certain day, Tim invested \$1,000 at 10 percent annual interest [#permalink]
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