A opens a recurring deposit account of Rs 200 p.m . How many instalments does he have to pay to get a maturity of Rs 5150? The bank pays a S.I of 7%p.a
 

Asked by saketagarwal.dbl | 19th Mar, 2017, 10:21: AM

Expert Answer:

begin mathsize 16px style Monthly space installment space left parenthesis straight P right parenthesis equals Rs. space 200
Rate space of space interest space left parenthesis straight r right parenthesis equals 7 percent sign
Maturity space values space left parenthesis MV right parenthesis equals Rs. space 5150
Let space the space number space of space months space be space straight n.
MV equals straight P left parenthesis straight n right parenthesis plus open square brackets fraction numerator Pn left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction cross times straight r over 100 cross times 1 over 12 close square brackets
rightwards double arrow 5150 equals left parenthesis 200 straight n right parenthesis plus open square brackets fraction numerator 200 straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction cross times 7 over 100 cross times 1 over 12 close square brackets
rightwards double arrow 5150 equals 200 straight n plus fraction numerator 7 straight n left parenthesis straight n plus 1 right parenthesis over denominator 12 end fraction
rightwards double arrow 61800 equals 2400 straight n plus 7 straight n squared plus 7 straight n
rightwards double arrow 7 straight n squared plus 2407 straight n minus 61800 equals 0
Using space fraction numerator negative straight b plus square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction space space or space you space could space just space factorise space to space find space the space values space for space straight n
rightwards double arrow 7 straight n squared plus 2557 straight n minus 168 straight n minus 61800 equals 0
rightwards double arrow left parenthesis 7 straight n plus 2575 right parenthesis left parenthesis straight n minus 24 right parenthesis equals 0
rightwards double arrow straight n equals fraction numerator negative 2575 over denominator 7 end fraction space or space straight n
Since space straight n space cannot space be space negative.
So comma space straight n equals 24.
Thus comma space the space number space of space installments space is space 24. end style

Answered by Rebecca Fernandes | 19th Mar, 2017, 01:14: PM