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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]

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New post 05 Jun 2012, 05:03
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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?

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Re: on may 1 of last year, jasmin invested X dollars in a new ac  [#permalink]

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New post 17 Jan 2013, 01:48
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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.

Answer D.

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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 30 Jun 2012, 23:46
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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.
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 05 Jun 2012, 09:32
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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 ac  [#permalink]

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New post Updated on: 17 Jan 2013, 01:39
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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.

Hence choice(D) is the answer.
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Originally posted by PrashantPonde on 17 Jan 2013, 01:35.
Last edited by PrashantPonde 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  [#permalink]

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New post 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]

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New post 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.

Hence choice(D) is the answer.



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
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 12 Jan 2014, 04:14
enigma123 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 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?



We're given X*0.05 = Interest after 1 month, so we have two unknowns (because even if we have more than 1 period, that's just an exponential relationship, and the exponent is never unknown)..

Isn't it simply easier to solve this like an algebraic translation instead of doing calculations? That way you only need to know what you need, not what the actual results are.

1) Solves for one of our unknowns, so it's clearly sufficient

2) Also solves for the same unknown as 1), but this time with a different exponent, so this is also sufficient.

So, answer is D. We can solve questions like these in 20 seconds with this approach, no calculation involved at all.
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On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post Updated on: 06 Sep 2016, 05:19
Bunuel chetan2u Can you please help me here

I thought with monthly compounding interest, your time value must be multiplied by 12? But we are getting 1 as the exponent. The formula that I am using is

I = P [(1+R/100)^n - 1]

I am not able to understand as to why n = 1? Is it because n = c*t = 12 *1/12 = 1?

Please confirm. Thanks!

Originally posted by keats on 06 Sep 2016, 04:36.
Last edited by keats on 06 Sep 2016, 05:19, edited 1 time in total.
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 06 Sep 2016, 04:54
macjas wrote:
Principal: $x
Rate (per year): 6% compounded monthly

Rate (per month): \(\frac{6%(per year)}{12(months)} = 0.5%\)


That should be the simplest part but why is it 6/12 and not .06/12
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 07 Sep 2016, 02:50
Keats wrote:
Bunuel chetan2u Can you please help me here

I thought with monthly compounding interest, your time value must be multiplied by 12? But we are getting 1 as the exponent. The formula that I am using is

I = P [(1+R/100)^n - 1]

I am not able to understand as to why n = 1? Is it because n = c*t = 12 *1/12 = 1?

Please confirm. Thanks!


Hi
standard is compounded annually and the formula you have written fits in there...
But if a question has compounded some period, look how many period are there and time will get multipled by that period and the rate will get divided by that...
If semiannually, two periods of 6 months in a year, one year will make n as 2 and rate as r/2..
Here it is monthly, so 12 periods in a month, so a year will make n as 12 and rate as 6/12..
But we are looking for only ONE month or 1/12 year, so n will be 1/12 * 12= 1..
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 08 Sep 2016, 00:43
Thanks chetan2u I have understood your point :)
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 08 Sep 2016, 00:50
IsabelleTreuille wrote:
macjas wrote:
Principal: $x
Rate (per year): 6% compounded monthly

Rate (per month): \(\frac{6%(per year)}{12(months)} = 0.5%\)


That should be the simplest part but why is it 6/12 and not .06/12


IsabelleTreuille Read his explanation carefully
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 11 Mar 2017, 01:50
enigma123 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 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?


Hi Guys,

I have a query. Both statements A and B says that the investment earned 'abc' $'s in ''INTEREST". Does this mean abc = 'Principal amount + Interest' or abc = 'Interest' ?

Many thanks for your help.
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 11 Mar 2017, 04:17
ruhigupta29 wrote:
enigma123 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 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?


Hi Guys,

I have a query. Both statements A and B says that the investment earned 'abc' $'s in ''INTEREST". Does this mean abc = 'Principal amount + Interest' or abc = 'Interest' ?

Many thanks for your help.


It's only interest, not principal + interest.
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Re: On May 1 of last year, Jasmin invested x dollars in a new  [#permalink]

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New post 21 May 2018, 16:51
enigma123 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 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.


We are given that Jasmin invested x dollars in a new account at an interest rate of 6 percent per year, compounded monthly, on May 1 of last year. In that case, the total amount A (principal plus interest) after m months will be A = x(1 + 0.06/12)^m or A = x(1.005)^m. Since the principal is x, then the total interest earned during the same period is A - x = x(1.005)^m - x = x(1.005^m - 1).

Statement One Alone:

As of June 1 of last year, the investment had earned $200 in interest.

We see that m = 1 since only 1 month passed from May 1 to June 1, so we can create the equation x(1.005^1 - 1) = 200. Without actually solving for x, we see that the equation is solvable for x. So statement one is sufficient.

Statement Two Alone:

As of July 1 of last year, the investment had earned $401 in interest.

We see that m = 2 since 2 months passed from May 1 to July 1, so we can create the equation x(1.005^2 - 1) = 401. Without actually solving for x, we see that the equation is solvable for x. So statement two is also sufficient.

Answer: D
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