A sum of Rs. 10 is given as a loan to be returned in 6 monthly installments at Rs.3. What is the rate of interest?

640%

NA

Solution:

Formula: Principal + S.I = Amount where,

S.I = Pnr/100

P is the principal in rupees,

n is time in years,

r is rate of interest in percentage.

Given: Principal = Rs.10, 6 months in year = 0.5 year.

So, Principal + S.I. = 10 + [ (10)(r)(0.5)/100 ]

= 10 + 5r/100

= 10 + r/20

Total effective payment,A

= (Rs.3 + interest on Rs.3 for 5 months) + (Rs.3 + interest on Rs.3 for 4 months)+.....+( Rs.3 + interest on Rs.3 for 1 month) + Rs.3

= [3 + (3)(5/12)(r)/100] + [3 + (3)(4/12)(r)/100] + .....+ [3 + [(3)(1/12)(r)/100] + 3

= [3 + 15r/1200] + [3 + 12r/1200] + .....+ [3 + 3r/1200] + 3

= 18 +( 15r/1200 + 12r/1200 + .....+ 3r/1200 )

= 18 + (3r/1200)(1 + 2 + 3 + 4 + 5 )

= 18 + (r/400)(15)

= 18 + 3r/80

Now, Principal + S.I. = Amount

=> 10 + r/20 = 18 + 3r/8

r /20 - 3r/80 = 18 - 10

4r - 3r /80 = 8

r /80 = 8

r = 80 × 8

r = 640%

So, the correct option is D). 640%