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Bob invested one half of his savings in a bond that paid simple intere

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Bunuel
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Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   21 Apr 2015, 05:46
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Bob invested one half of his savings in a bond that paid simple interest for 3 years and received $825 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 3 years at the same rate of interest and received $1001 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

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Celestial09
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   21 Apr 2015, 06:14
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Hi,
IMO it should be E 20%
reason: though I did this kind of question first time so need to know if its a correct answer and easy way to solve?
simple interest 825/3 = 275 per year
simple interest 275 275 275
compound interest for first year will be same as simple interest that is 275
total difference in interest 1001-825 = 176/3 approx 59 per year but make sure that we are assuming here by approximation rule
so it obvious that for the second year the difference will be less than 59. say 55
55/275 is 20%
now check the compounding of each year at this rate. so it will come up as 1001.

regards
celestial


kudos if its a correct solution


Bunuel wrote:
Bob invested one half of his savings in a bond that paid simple interest for 3 years and received $825 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 3 years at the same rate of interest and received $1001 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.
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gamerssc
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   23 Apr 2015, 00:23
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Bunuel wrote:
Bob invested one half of his savings in a bond that paid simple interest for 3 years and received $825 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 3 years at the same rate of interest and received $1001 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.


Need solution for this question, Assuming from options from 2nd yr interest on wards doesn't seem feasible
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Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   27 Apr 2015, 03:28
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Bunuel wrote:
Bob invested one half of his savings in a bond that paid simple interest for 3 years and received $825 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 3 years at the same rate of interest and received $1001 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.


CHECK VERITAS PREP OFFICIAL SOLUTION HERE:
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Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   10 Apr 2020, 00:26
Bunuel wrote:
Bob invested one half of his savings in a bond that paid simple interest for 3 years and received $825 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 3 years at the same rate of interest and received $1001 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.



Bunuel, VeritasKarishma, chetan2u

I understand this problem and the solution presented. However, I wanted to ask what happens when the number of years is significantly larger, like 10 years, 20 years and so on? I tried following @VeritasKarishma's method to derive CI for years 4 and 5 but its definitely getting a little confusing for higher numbers. Please let me know.
Thanks
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KarishmaB
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   12 Apr 2020, 01:04
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sreddy07 wrote:
Bunuel wrote:
Bob invested one half of his savings in a bond that paid simple interest for 3 years and received $825 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 3 years at the same rate of interest and received $1001 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.



Bunuel, VeritasKarishma, chetan2u

I understand this problem and the solution presented. However, I wanted to ask what happens when the number of years is significantly larger, like 10 years, 20 years and so on? I tried following @VeritasKarishma's method to derive CI for years 4 and 5 but its definitely getting a little confusing for higher numbers. Please let me know.
Thanks


Here is what SI vs CI looks like for upto 4 years. Note that in the fourth year itself, it has gotten far more complicated.

Attachment:
Screenshot 2020-04-12 at 13.29.52.png
Screenshot 2020-04-12 at 13.29.52.png [ 58.69 KiB | Viewed 5315 times ]


You are not expected to handle this kind of complexity without a calculator so don't worry about it.

As for this question, I would just try to approximate.
r% of r% of 275 will be much smaller than r% of 3*275 so I will ignore it.

r% of 3*275 = 176

So r is about 21%. But since we ignore a small component, r would be smaller so 20%.
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   25 Jul 2021, 15:04
Hi VeritasKarishma and Bunuel, can you explain the part please:

R% of 275 + R% of (275 + 275 + R% of 275)
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KarishmaB
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Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   Updated on: 25 Aug 2023, 01:46
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testtakerstrategy wrote:
Hi VeritasKarishma and Bunuel, can you explain the part please:

R% of 275 + R% of (275 + 275 + R% of 275)



Check out this post https://anaprep.com/arithmetic-solving- ... -interest/

Originally posted by KarishmaB on 25 Jul 2021, 23:59.
Last edited by KarishmaB on 25 Aug 2023, 01:46, edited 1 time in total.
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Vep22
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   14 Nov 2021, 23:35
VeritasKarishma wrote:
testtakerstrategy wrote:
Hi VeritasKarishma and Bunuel, can you explain the part please:

R% of 275 + R% of (275 + 275 + R% of 275)



Check out these two posts on our Blog first:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... imple-one/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... -the-gmat/

They explain the concept of earning interest on interest in detail.


Unable to get it for https://gmatclub.com/forum/bob-invested ... 96540.html.

Since its two yrs the exprression must be 55 = 275( interest of first yr) + R% (275+R%of 275) and not 55 = R%of 275. Pls elaborate
Let me know if you still have doubts.
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Bob invested one half of his savings in a bond that paid simple intere [#permalink] New post   08 Aug 2023, 04:59
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KarishmaB wrote:
testtakerstrategy wrote:
Hi VeritasKarishma and Bunuel, can you explain the part please:

R% of 275 + R% of (275 + 275 + R% of 275)



Check out this post on my Blog first:
https://anaprep.com/arithmetic-solving- ... -interest/

It explains the concept of earning interest on interest in detail.
Let me know if you still have doubts.
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Bob invested one half of his savings in a bond that paid simple intere [#permalink]
08 Aug 2023, 04:59
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