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

Question

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.

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

Kudos for a correct  solution .

Celestial09 · Accepted Answer

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

gamerssc · Answer

Need solution for this question, Assuming from options from 2nd yr interest on wards doesn't seem feasible

Bunuel · Answer

CHECK VERITAS PREP OFFICIAL SOLUTION  HERE :

sreddy07 · Answer

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

KarishmaB · Answer

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. Screenshot 2020-04-12 at 13.29.52.png 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%.

testtakerstrategy · Answer

Hi  VeritasKarishma  and  Bunuel , can you explain the part please:

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

KarishmaB · Answer

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

Vep22 · Answer

KarishmaB · Answer

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards