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

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

Answer D.

-Shalabh Jain
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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.

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

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.

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?

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

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.

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!

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

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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Thanks chetan2u I have understood your point

IsabelleTreuille Read his explanation carefully

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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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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