Jeramiah invests his savings of $120,000 by dividing it between two in

Question

Jeramiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?

A. 3
B. 4
C. 5
D. 6
E. 7

A. 3
B. 4
C. 5
D. 6
E. 7

Shobhit7 · Accepted Answer

Principal: 120k
Account A: 90K, Weightage 3/4
Account B: 30K, Weightahe 1/4
Net Interest: 3636 on 120K , (3636/120,000)*100= 3.03% Compound, assume approx 3% SI

Case 1: Test Account B with r=2%
1/4*2 + 3/4*r = 3
r= 10/3= 3.33%, no match in ans choices

Case 2: Test Account A with r=2%
1/4*r + 3/4*2 = 3
r= 6% Ans D

KrishnakumarKA1 · Answer

Hi,

It is an interesting question.

Given: 120000 is split into two interest earning accounts.

First saving, lets call it as A = ¾(120000) = 90000

Other saving, lets call it as B = ¼(120000) = 30000

Given, total interest earned from this account is 3636 at the end of the year.

Also, given one account earns 2 percent annual interest and both compounding semi-annually.

Question: What is the rate of interest of the other account?

First task to figure out here is, which account earns two percent annual interest. Definitely it has to be the account A = 90000.

Because, lets suppose B = 30000 is the account which earns 2% annual interest which compounded semi-annually.

Compound semi-annually means two times in a year,

That’s is if “r” is the annual rate interest, then semi-annually it is r/2

(r/2)% of Amount + (r/2)% of Amount + (r/2)% of interest got in the six month period = interest amount for the year.

So interest amount earned is,

1% of 30000 + 1% of 30000 + 1% of 300 = 300 + 300 + 3 = 603

And the remaining interest should have been earned from the account A = 90000, but if you look at the answers, the rate of interest is very high and it will give you a value more than 3600.

Maybe only answer choices which may looks suitable is A = 3%, but this will give you the interest amount in decimal values. i.e.,

1.5% of 90000 + 1.5% of 90000 + 1.5% of 1350 = 1350 + 1350 + 20.25 = 2720. 25. Which contradicts the total amount 3636.

So, the 2% percent annual interest should be from the account A = 90000.

So, the interest amount should be,

1% of 90000 + 1% of 90000 + 1% of 900 = 900 + 900 + 9 = 1809.

So the remaining interest amount = 3636 – 1809 = 1827.

So, if you look at the answer choices, roughly 6/100 * 30000 = 1800. So it has to be the answer.

3% of (30000) + 3% of (30000) + 3% of 900 = 900 + 900 + 27 = 1827.

So the answer is D.

Hope this helps.

aviddd · Answer

Thanks for the detailed answer. Is there a faster way to solve, instead of doing a trial and error?

Pranithare · Answer

No need of trail and error.
Let c=I1+I2
First calculate the combined interest(C) , it is 3636/120000=3.03 %
As we know from question one account has 2% ,so calculate the 3/4 th amount(90*1000) with 2 % we get 1800=I1
C-I1=1836
Now 1836/30*1000=6.12

Nups1324 · Answer

Hi  Bunuel ,

If the path to arrive at the answer is via 1827/30000, then don't you think the question should mention the word "approximately"?

Because 1827/30000 is 0.0609 which is 6.09% and not exactly 6%.

I got 6.09% within 2 mins but then I was stuck due to the absence of the word "approximately". I spent 2 more mins to recheck and arrive at a round figure percent answer.

Please help me regarding this small but important doubt.

Tagging others just in case Bunuel is busy or offline. 
 yashikaaggarwal   chetan2u   GMATinsight   ScottTargetTestPrep   IanStewart

Thank you

Posted from my mobile device

GMATinsight · Answer

Nups1324

You are absolutely correct. When question expects the approximate answer then the word approximately must be available in question

yashikaaggarwal · Answer

As Been said above, having "approximate" word will make question more easier to read. But having 6.09 as answer denotes closer interger 6 only, since we don't have 6.1 or 6.05 in the options. 6 is the only feasible option so I don't think 6 approximate would had changed anything.

IanStewart · Answer

If a real GMAT question is asking for an approximate value, the question will always need to tell you that. This question is not asking for an approximation, though -- the correct answer is exactly 6%. The key phrase in the question is "both accounts are compounded semiannually". In your answer, you haven't accounted for the compounding.

I'd still solve the problem by estimating and ignoring the compounding, because the compounding here will have almost no effect.

Nups1324 · Answer

Thank you for your replies yashikaaggarwal GMATinsight IanStewart IanStewart Oh yes.. you're absolutely correct... dividing 1827 by 30000 will give simple interest. The compounding effect is missing there. So the conclusion is that the GMAT will always mention he word "approximately" when we indeed have to approximate.. this question is not about approximation.. So the method of dividing 1827 by 30000, mentioned above by my fellow users, is not ideal for CI but it is helpful in narrowing our search and then approximating.. or is it completely wrong..? Thank you

Posted from my mobile device

IanStewart · Answer

Yes, any real GMAT question that only wants an approximation will need to mention that in the question. There are some prep company questions I've seen that don't observe that requirement, however, and those questions are problematic.

I wouldn't solve the question by computing 1827 and dividing by 30,000, but that method is fine here. When you compound a small interest rate only once, the effect is negligible, so you can liberally estimate here without compromising your ability to recognize the correct answer.

The problem is just a weighted average, though. Since the compounding will barely affect anything, I'd just round things off. The overall interest rate is roughly 3%. The larger group earns a 2% interest rate. If you know the method of "alligation", you'd then draw this number line:

---2%----3%------------------x%----

where the distances above to the middle number are in a 1 to 3 ratio, the same ratio as the sizes of the groups. The smaller distance, from 2 to 3, is equal to 1, so the larger distance, from 3 to x, must be 3, and x = 6%. So the right answer is either 6% or very close to it, and D must be correct.

ramlala · Answer

Jeramiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?

A. 3
B. 4
C. 5
D. 6
E. 7

Prethinking: Given interest rate is 2% and answer choice is > than 2%.

Principle amount for lower interest rate @2%: (3/4)120,000 = 90,000
Interest amount @2% (Approx) = 90,000*2% = 1800

Balance interest amount = 3636 - 1800 = 1800 (Approx)
Balance principle amount = (1/4) 120,000 = 30,000

Interest rate = (1,800/30,000)*100 = 6%

Ans = D

Remarks: don't go for actual interest amount (36) as the differance in answer is 1% (of 30,000) that is 300.

ScottTargetTestPrep · Answer

As it has already been mentioned, 1827/30,000 will yield a close but slightly higher interest rate than the actual interest rate. This figure gives you the answer assuming the interest was simple and in order to collect the same interest as the compound interest, simple interest rate needs to be higher. How high depends on the number of times the interest is compounded.

Here's how you can get the exact answer of 6%:

Looking at the answer choices, we understand that the account that pays 2% annual interest is the account that earns lower interest, so $90,000 was invested at 2%. At the end of the year, the account will be worth:

90,000 * (1 + 2/200)^2

90,000 * 1,01^2

90,000 * 1,0201

91,809

So, the interest collected from the 2% account is 91,809 - 90,000 = $1,809. Thus, 3,636 - 1809 = $1,827 was collected from the other account. To find the interest rate which will yield an interest of $1,827 from a principal of 120,000 - 90,000 = 30,000, we let x be the interest rate and solve:

30,000 * (1 + x/200)^2 = 31,827

(1 + x/200)^2 = 31,827/30,000 = 1,0609

1 + x/200 = 1,03

x/200 = 0,03

x = 6

So, the other account paid 6% interest. While this method gives you the exact answer, I recommend using the simple interest method and keeping in mind that the value obtained assuming the interest was simple will be slightly higher.

Bambi2021 · Answer

1 % of 90 000 = 900
1 % of 900 = 9

1809 from account A.

then I started with C,

1 % of 30 000 = 300
5 % = 1500

must be higher, so D gives

6 % = 1800

Slightly higher when compounded, pick D.

norafateh · Answer

The amount invested in the lower interest account is (3/4) * $120,000 = $90,000.

The amount invested in the higher interest account is (1/4) * $120,000 = $30,000.

Jeramiah makes $3,636 in interest by the end of the year, so:
0.75⋅90,000⋅A+0.25⋅30,000⋅B=3,636
Substituting the expressions for A and B:
0.75⋅90,000⋅((1+ 100x)2−1)+0.25⋅30,000⋅((1+ 100y ) 2 −1)=3,636

Solving this equation will give us the value of y, which represents the interest rate for the higher interest account.

After performing the calculations, we find that y is approximately 5.93.

So, the interest rate for the other account (the higher interest account) is approximately 5.93 percent.

mGupta074 · Answer

Given amount 120000, so 3/4 is 90000 and 1/4 is 30000
90000 is compounded semiannually at 2%, for first 6 month interest is 1800, adding this to 90000,
91800 is compunded at 2% for next 6 months and total interest will be 1836

So he can earn 1800$ on other investment, which is 30000

1800/30000 = 6%

Jeramiah invests his savings of $120,000 by dividing it between two in

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