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# On May 1 of last year, Jasmin invested x dollars in a new

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On May 1 of last year, Jasmin invested x dollars in a new [#permalink]  05 Jun 2012, 05:03
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83% (01:46) correct 16% (00:56) wrong based on 1 sessions
On May 1 of last year, Jasmin invested x dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x?

(1) As of June1 of last year, the investment had earned $200 in interest. (2) As of July 1 of last year, the investment had earned$401 in interest.

I got this right but it was the guess work, Can someone please explain the mathematical solution to this?
[Reveal] Spoiler: OA

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Re: On May 1 of last year, Jasmin invested x dollars in a new [#permalink]  05 Jun 2012, 09:32
I think you can just use the formula: Future Value = Present Value x (1 + (interest rate/12))^number of months

In both cases, they give you Future Value (Present Value + Interest Earned), they give you the interest rate (6.0% annually), and they give you the number of months to compound over, so you can solve for the Present Value in both cases
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Re: On May 1 of last year, Jasmin invested x dollars in a new [#permalink]  30 Jun 2012, 23:46
1
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Principal: $x Rate (per year): 6% compounded monthly Rate (per month): \frac{6%(per year)}{12(months)} = 0.5% (1) As of June1 of last year, the investment had earned$200 in interest.

In one months time, the interest earned is $200: x * (\frac{0.5}{100}) = 200. From this, we can find out the value of x. Hence, A is sufficient (2) As of July 1 of last year, the investment had earned$401 in interest.

In two months, the interest earned on the new principal is $401: x * (1 + \frac{0.5}{100})*(\frac{0.5}{100}) = 401. Above, the expression x * (1 + \frac{0.5}{100}) represents the principal after the end if the first month i.e the initial principal+one month's worth of interest. This is enough to compute the value of x. B is also sufficient. Thus, the answer is D, both statements alone are sufficient. Senior Manager Joined: 29 Nov 2012 Posts: 277 Followers: 1 Kudos [?]: 12 [1] , given: 239 on may 1 of last year, jasmin invested X dollars in a new ac [#permalink] 16 Jan 2013, 23:29 1 This post received KUDOS on may 1 of last year, jasmin invested X dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x? 1) as of june 1 of last year, the investment had earned$200 in interest
2) as of july 1 of lasy year, the investment had earned $401 in interest. I know its a basic question, you don't really need to solve it but I'm interested in the detailed approach in case I see a problem solving question of this type. Senior Manager Joined: 27 Jun 2012 Posts: 413 Followers: 23 Kudos [?]: 193 [3] , given: 171 Re: on may 1 of last year, jasmin invested X dollars in a new ac [#permalink] 17 Jan 2013, 01:35 3 This post received KUDOS Interest Rate per month: 6%/12 months = 0.5% (monthly) (1) As of June1 of last year, the investment had earned$200 in interest.
SUFFICIENT: interest earned in one month = $200 Principal * (0.5/100) = 200 Principal amount =$40000. Hence sufficient.

(2) As of July 1 of last year, the investment had earned $401 in interest. SUFFICIENT: interest earned in two months =$401

Principal * (1 + 0.5/100)*(0.5/100) = 401
We can solve this equation to find out Principal amount. Hence sufficient.

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Last edited by PraPon on 17 Jan 2013, 01:39, edited 2 times in total.
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Re: on may 1 of last year, jasmin invested X dollars in a new ac [#permalink]  17 Jan 2013, 01:35
fozzzy wrote:
on may 1 of last year, jasmin invested X dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x?

1) as of june 1 of last year, the investment had earned $200 in interest 2) as of july 1 of lasy year, the investment had earned$401 in interest.

I know its a basic question, you don't really need to solve it but I'm interested in the detailed approach in case I see a problem solving question of this type.

on-may-1-of-last-year-jasmin-invested-x-dollars-in-a-new-133937.html?fl=similar
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Re: on may 1 of last year, jasmin invested X dollars in a new ac [#permalink]  17 Jan 2013, 01:48
1
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fozzzy wrote:
on may 1 of last year, jasmin invested X dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x?

1) as of june 1 of last year, the investment had earned $200 in interest 2) as of july 1 of lasy year, the investment had earned$401 in interest.

I know its a basic question, you don't really need to solve it but I'm interested in the detailed approach in case I see a problem solving question of this type.

Statement 1-

Monthly C.I.(Compd. Int.) = 6/12=0.5% per month;
When there is only one period for calculation, then C.I.= S.I.(simple Int.). In this question May to June is one month only.

We know that SI=P*r*t/100 => 200=P*0.5*1/100 => P can be derived. There is no need to calculate exact value in DS question.Just make sure there is a unique value. Sufficient.

Statement 2-

From May to July there are 2 periods, so this is the case of CI rather SI.

We know that CI=P(1+r/100)^n => n= # of periods = 2 months => 401=P(1+0.5/100)^2 => P can be derived. There is no need to calculate exact value. Sufficient.

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Re: on may 1 of last year, jasmin invested X dollars in a new ac [#permalink]  17 Jan 2013, 04:23
fozzzy wrote:
on may 1 of last year, jasmin invested X dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x?

1) as of june 1 of last year, the investment had earned $200 in interest 2) as of july 1 of lasy year, the investment had earned$401 in interest.

I know its a basic question, you don't really need to solve it but I'm interested in the detailed approach in case I see a problem solving question of this type.

Merging similar topics.

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Re: On May 1 of last year, Jasmin invested x dollars in a new [#permalink]  25 Mar 2013, 16:04
I thought with monthly compounding interest, your time value must be multiplied by 12? But we are getting 1 as the exponent, is this because you are multiplying 12* 1/12 for the number of periods being just one month?
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Re: on may 1 of last year, jasmin invested X dollars in a new ac [#permalink]  25 Mar 2013, 16:10
PraPon wrote:
Interest Rate per month: 6%/12 months = 0.5% (monthly)

(1) As of June1 of last year, the investment had earned $200 in interest. SUFFICIENT: interest earned in one month =$200

Principal * (0.5/100) = 200

Principal amount = $40000. Hence sufficient. (2) As of July 1 of last year, the investment had earned$401 in interest.
SUFFICIENT: interest earned in two months = \$401

Principal * (1 + 0.5/100)*(0.5/100) = 401
We can solve this equation to find out Principal amount. Hence sufficient.

Also can you explain how you are able to get to principal * (0.5/100) = 200? I guess I am trying to go by the formula which is x(1 + (6/100) / 12) ^ n - x but i dont understand how you get to that
Re: on may 1 of last year, jasmin invested X dollars in a new ac   [#permalink] 25 Mar 2013, 16:10
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