SOLUTION: A student may buy a bicycle for Rs. 1600 cash down and take delivery at once, or he can pay Rs. 650 cash down, Rs. 500 at the end of a month and another sum of Rs. 500 at the end

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Question 1039213: A student may buy a bicycle for Rs. 1600 cash down and take delivery at once, or he can pay Rs. 650 cash down, Rs. 500 at the end of a month and another sum of Rs. 500 at the end of two months. What rate of SI does the merchant charge under the second plan?
a) 40 % b) 41 % c) 42 % d) 43 %
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe this involves interest rate compounded monthly where your payments are at the end of each month.

given that assumption , then the answer appears to be 42%.

here's why.

the price of the bicycle is 1600.
you put 650 down.
you are therefore taking a loan out or 950.
your payments are 500 at the end of each month for 2 months.

i used the following online financial calculator to come up with the results.
http://arachnoid.com/finance/index.html

i made the following entries.

present value = -950
future value = 0
number of periods = 2
payment amount = 500
payment at end.
i then clicked on ir and the calculator told me that the interest rate was 3.488833%.

the number of periods was in months.
the interest rate shown by the calculator was interest rate per month as a percent.

to get the annual percentage rate, the monthly interest rate had to be multiplied by 12.

after doing that, i got an annual percentage rate of 41.8655996% which rounds to 42%.

when you use the calculator, you have to remember that, if present value is negative, then future value or payment amount has to be negative, or vice versa.

this has to do with cash flow analysis where money is going out and money is coming back in.

i should have shown present value as positive and payment amount as negative.
it didn't really matter as far as the calculator was concerned, but in real life that would have been more accurate since i borrowed 950 which was money coming in and i paid out the payments which was money going out.

i tried simple interest formula first but didn't come up with any of the selections so then i tried remaining balance payments using the calculator and i was able to come up with one of the selections.

i'm not sure if it was done correctly, but it does give you an answer that corresponds to one of your selections.

here is a picture my inputs to the calculator provided.

$$$

the ir button is what i pressed after making the inputs in the other fields.