On what sum will the difference between simple and compound

Question

Hi,

I am unable to solve the below mentioned question as well not able to understand thr answer that is provided. request members and experts to provide solution.

On what sum will the difference between simple and compound interest for 3 years at 5 percent per annum amount to 12.20?

answer is 1600.

thanks and regards,

harish

mikemcgarry · Answer

Dear Harish, I'm happy to help. :-)

First of all, I'll say watch the free Magoosh blog, https://magoosh.com/gmat/ because I just wrote an extensive article on simple & compound interest, with practice questions, and that will go live on the blog in a week or so. Understand, first of all, that this question is not really a GMAT question as is, because it would require a calculator to solve. If five answer choices were given, we would be able to use backsolving to determine an answer. See: https://magoosh.com/gmat/2013/backsolving-on-gmat-math/ I will just start with the value $1600 and backsolve from this, showing that it works. First, simple interest. 1% of 1600 is $16, so 5% is 5*16 = $80. That's simple interest for one year. In three years, that's 3*80 = $240. Now, compound interest. The amount will experience a 5% increase three times. The multiplier for a 5% increase is 1.05. For more on percent increases as multipliers, see: https://magoosh.com/gmat/2012/understand ... -the-gmat/ The total amount, principle plus compound interest, after three years is 1600*(1.05)^3 = $1852.20 (I used a calculator for that.) That's $252.20 in interest. That's a 252.20 - 240 = $12.20 difference between simple & compound interest. Understand, my friend, it's very very easy to create compound interest questions that only could be solved with a calculator. It's a bit trickier to write high quality compound interest questions that can be solved entirely without a calculator, which are amenable to estimation and backsolving and other approximation methods. The blog that will be release on the Magoosh blog in a week or so will have a few high quality questions of this sort. Here's another question of that order: Cindy invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years? (A) $10079.44 (B) $10815.83 (C) $12652.61 (D) $14232.14 (E) $20598.11 Let me know if you would like an explanation of this question. OA = (B) Mike :-)

KarishmaB · Answer

To solve this question, you need to understand how simple and compound interest are different. Note that it is easy to solve for their difference after 2 years but it gets trickier as you increase the number of years. I have discussed these concepts in this post: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... imple-one/ Compound interest differs by simple in that it gives interest on interest earned too. In the first year, both compound and simple give the same interest (assuming annual compounding). In the second year, compound interest includes interest on the interest earned in the first year too. Say, initial amount is D. ______________SI____________________CI 1st year______0.05D_________________0.05D 2nd Year____2*0.05D________________ 2*0.05D + 0.05*0.05D (Interest earned on last year's interest) 3rd Year____3*0.05D________________3*0.05D + 0.05*0.05D + .05( 2*0.05D + 0.05*0.05D ) The difference in the SI and CI in third year is 0.05*0.05D + .05(2*0.05D + 0.05*0.05D) = 12.2 (25/10000)(3D + 0.05D) = 12.2 D = 4880/3.05 If you assume the denominator is 3, you get 1600 something. Ignore the something since denominator is greater than 3 to get 1600.

harishbiyani · Answer

Hi Mike,

Thanks for your explanation. It was helpful.

Regarding this question that you have posted; is the answer Option B?

This is how i calculated the answer:

= 10,000*101.98/100*101.98/100*101.98/100*101.98/100
= 10.198 * 10.198 * 10.198 * 10.198
~ 10.2 * 10.2 * 10.2 * 10.2
~ 10816

The approximated answer is 10, 816 so i choose option B

Let me know if there is any other faster way to answer this question. It would be great to learn.

Also, could you please tell me what was the level of the question?

Thanks,
Harish

harishbiyani · Answer

Thanks Krishna for your explanation too.

I had never used this method before. I hope, i can use your method in some complex problems.

Thanks and Regards,
Harish

KarishmaB · Answer

Ok, then use the method I discussed above to solve the question given by Mike orally. Think - what is the difference between SI and CI? What happens to this difference if rate of interest is very low such as approx 2%? Can you easily approximate the answer without lifting a finger?

harishbiyani · Answer

I mis- spelled your name as Krishna instead of Karishma.

Sorry for that.

On what sum will the difference between simple and compound

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