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

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Jeramiah invests his savings of $120,000 by dividing it between two in  [#permalink]

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New post Updated on: 26 Sep 2018, 21:48
3
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

57% (01:38) correct 43% (03:14) wrong based on 42 sessions

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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

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Originally posted by Sreyoshi007 on 26 Sep 2018, 21:46.
Last edited by Bunuel on 26 Sep 2018, 21:48, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Jeramiah invests his savings of $120,000 by dividing it between two in  [#permalink]

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New post 27 Sep 2018, 00:22
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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.
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Re: Jeramiah invests his savings of $120,000 by dividing it between two in  [#permalink]

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New post 14 Oct 2018, 13:55
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
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Re: Jeramiah invests his savings of $120,000 by dividing it between two in &nbs [#permalink] 14 Oct 2018, 13:55
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