Problem Solving

A sum of $10 is lent to be returned in 11 monthly installments of $1 each, interest being simple. The rate of interest is:

100/11 %
10 %
11 %
230/11 %
240/11%

I'm not sure if I've missed a trick or wrongly interpreted the question, but I think its quite straight forward.

Principal = $10
Interest earned = $11 - $10 = $1

Interest rate over the lending period = 1/10 = 10%.

Choose B.

-BM-

bluementor wrote:I'm not sure if I've missed a trick or wrongly interpreted the question, but I think its quite straight forward.

Principal = $10
Interest earned = $11 - $10 = $1

Interest rate over the lending period = 1/10 = 10%.

Choose B.

-BM-

You have 500% missed the question met? Think? Read? Re-read? $10 is returned $1 a month for 11 month. The $1 paid in month 1 is for 10 month the one for 11th none?

Do let me know if u still miss it. its a very tricky question...

Not that tricky too anyways here's the solution in my opinion

simple interest = PRT where P = Principal = $10, R = Rate, T =number of periods = 11/12 year

1 = 10*11*R/(100*12)

R = 120/11

= 10.9% or 11% (round up)

Hi
doofus, why do you assume that the period of the rate is one year (12 month)?

You would be alright if the question asked the "12 month rate" ... but in this case i´m not sure, correct me if i´m wrong.

wht is the OA?

I solved similar to dumbdoofus and got 120/11 or approx 11% as the answer.

pls post the OA

keizer Soze wrote:Hi
doofus, why do you assume that the period of the rate is one year (12 month)?

You would be alright if the question asked the "12 month rate" ... but in this case i´m not sure, correct me if i´m wrong.

when the period is not mentioned for the interest rate then it is taken as for a year.. if it was monthly or even bimonthly, then it would be explicitly mentioned as interest rate is 5% per 30 days or 5% per 60 days..

so anytime, just the interest rate is given, please take it for one year.

Now lets assume that the interest rate is monthly for just the sake of clarifying your doubt..
then I have
1 = 10.r.11/100 or an interest rate of 10/11 = 0.91% which is none of the answer choices.

Hope this makes it clear..

Ok doofus, it´s good to know that!

The last one: can I round up a number when I have other solutions that are not integers?

OK OA is E

Here is the way to solve it:

SI = Simple Interest

$10 + SI on $10 for 11 months=$ 11 + SI of $1 for(1+2+3+4+..+10) months
10 + SI on $10 for 11 months= 11 + SI of $1 for 55 months
10 + SI on $1 for 10*11 months= 11 + SI on $1 for 55 months

SI on $1 for 55 months = 1

Rate = 100*12/(1*55) = E

Simple Interest Formula

Principal*Rate*T = Interest Paid

T= number of years

P = 10
T = 11/12
Interest Paid = 1

10*r*(11/12) = 1

r = 12/110

Approximately 11 ( you have to round up)

I dont think the GMAT would usually force you to make an assumption to round up like this, unless it explicity tells you to.

maihuna wrote:OK OA is E

Here is the way to solve it:

SI = Simple Interest

$10 + SI on $10 for 11 months=$ 11 + SI of $1 for(1+2+3+4+..+10) months
10 + SI on $10 for 11 months= 11 + SI of $1 for 55 months
10 + SI on $1 for 10*11 months= 11 + SI on $1 for 55 months

SI on $1 for 55 months = 1

Rate = 100*12/(1*55) = E

maihuna, i've seen this problem somewhere long back and am sure that your method is correct. but i can not understand the logic. could you please explain a little bit?

maihuna wrote:OK OA is E

Here is the way to solve it:

SI = Simple Interest

$10 + SI on $10 for 11 months=$ 11 + SI of $1 for(1+2+3+4+..+10) months
10 + SI on $10 for 11 months= 11 + SI of $1 for 55 months
10 + SI on $1 for 10*11 months= 11 + SI on $1 for 55 months

SI on $1 for 55 months = 1

Rate = 100*12/(1*55) = E

I am sorry buddy.. just can't get it.. please elaborate in simpler terms so that everyone benefits..