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# A bicycle is sold for 3,000 cash or for Rs 1,000 cash down payment followed by two monthly installments of Rs 1024 each. Compute the rate of interest charged under the installment scheme.

Last updated date: 23rd Mar 2023
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Hint- Use the basic formula ${\text{Interest = }}\dfrac{{P \times R \times T}}{{100}}$, where P
is the Principle amount,R is the rate of interest, and T is the time duration.

There are two modes that are firstly you give cash RS 3000 or pay Rs 1000 down payment in the initial stages to get the bicycle.
Hence, ${\text{Principal amount = Rs}}\left( {3000 - 1000} \right) = 2000{\text{ Rs}}$
Now in case someone opts for down payment then they have to give Rs 1024 as installments for 2 months.
Hence, ${\text{Interest = (Time of installment}} \times {\text{Amount of installment) - Principal amount}}$
So, ${\text{Interest = 2}} \times {\text{1024 - 2000 = 2048 - 2000 = 48 Rs}}$
Now we know that ${\text{Interest = }}\dfrac{{P \times R \times T}}{{100}}$where P is principal value, R is rate of interest, T is duration of installments.
So substituting values
${\text{48 = }}\dfrac{{2000 \times R \times 2}}{{100 \times 12}}$ As we are taking time duration in years hence we have ${\text{T = }}\dfrac{2}{{12}}$
On solving we get ${\text{R = }}\dfrac{{48 \times 100 \times 12}}{{2000 \times 2}} = 14.4\%$

Note- While computing interest problems always keep hold of formulae of interest and always take time duration in terms of years and not months otherwise you may land up on the wrong answer.