Mamta has two options to buy a house
(i) She can pay a lumpsum amount of Rs 2200000.
(ii) She can pay Rs 400000 cash and balance in 18 annual instalments of Rs 100000 plus 10% interest on the unpaid amount.
She prefers the option (i) and donates 50% of the difference of the costs in the above two options to national Relief Fund.
(a) What amount was donated to National Relief Fund?
(b) By choosing to pay a lumpsum amount and donating 50% of the difference to national Relief Fund. Which value is depicted by Mamta?
Dear Student,
Please find below the solution to the asked query:
Given : Cost of house = Rs . 2200000
i ) She can pay lumpsum amount of Rs. 2200000 .
ii ) She pay Rs . 400000 and balance in 18 annual instalment of Rs . 100000 + 10 % of unpaid amount ,
Here unpaid amount = 2200000 - 400000 = Rs. 1800000
So
Amount of first instalment = 100000 + 10 % of 1800000 = 100000 + (10/100)(1800000 ) = 100000 + 180000 = Rs. 280000
And
Amount of second instalment = 100000 + 10 % of 1700000 = 100000 + (10/100)(1700000 ) = 100000 + 170000 = Rs. 270000
And
Amount of third instalment = 100000 + 10 % of 1600000 = 100000 + (10/100)(1600000 ) = 100000 + 160000 = Rs. 260000
Here , We get instalment in A.P. : 280000 , 270000 , 260000 , . . .
Here first term = a = 280000 and Common difference = d = 270000 - 280000 = - 10000
We know sum n terms in A.P. : Sn = (n/2)[2a + ( n - 1 ) d ] , So
Cost of house after all instalments = 400000 + ( 18/2 )[ 2 ( 280000 ) + ( 18 - 1 ) ( -10000 ) ]
= 400000 + 9 [ 560000 + ( 17 ) ( -10000 ) ]
= 400000 + 9 [ 560000 - 170000 ]
= 400000 + 9 [ 390000 ]
= 400000 + 3510000
= 3910000
So,
Difference between both options = 3910000 - 2200000 = Rs .1710000
a ) Amount paid to national relief fund = 50 % of 1710000 = ( 50/100)1710000 = ( 50 )17100 = Rs . 855000 ( Ans )
b ) By doing such transaction Mamta shows her caring nature .
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given : Cost of house = Rs . 2200000
i ) She can pay lumpsum amount of Rs. 2200000 .
ii ) She pay Rs . 400000 and balance in 18 annual instalment of Rs . 100000 + 10 % of unpaid amount ,
Here unpaid amount = 2200000 - 400000 = Rs. 1800000
So
Amount of first instalment = 100000 + 10 % of 1800000 = 100000 + (10/100)(1800000 ) = 100000 + 180000 = Rs. 280000
And
Amount of second instalment = 100000 + 10 % of 1700000 = 100000 + (10/100)(1700000 ) = 100000 + 170000 = Rs. 270000
And
Amount of third instalment = 100000 + 10 % of 1600000 = 100000 + (10/100)(1600000 ) = 100000 + 160000 = Rs. 260000
Here , We get instalment in A.P. : 280000 , 270000 , 260000 , . . .
Here first term = a = 280000 and Common difference = d = 270000 - 280000 = - 10000
We know sum n terms in A.P. : Sn = (n/2)[2a + ( n - 1 ) d ] , So
Cost of house after all instalments = 400000 + ( 18/2 )[ 2 ( 280000 ) + ( 18 - 1 ) ( -10000 ) ]
= 400000 + 9 [ 560000 + ( 17 ) ( -10000 ) ]
= 400000 + 9 [ 560000 - 170000 ]
= 400000 + 9 [ 390000 ]
= 400000 + 3510000
= 3910000
So,
Difference between both options = 3910000 - 2200000 = Rs .1710000
a ) Amount paid to national relief fund = 50 % of 1710000 = ( 50/100)1710000 = ( 50 )17100 = Rs . 855000 ( Ans )
b ) By doing such transaction Mamta shows her caring nature .
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards