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Given : P = Rs. 8,000, R = 5%, T = 2 years
For simple interest,
S.I. = `[ "P" xx "R" xx "T"]/100`
= `[8,000 xx 5 xx 2]/100`
= Rs. 800
For compound interest,
`"A" = "P"( 1 + r/100 )^n`
`"A" = 8,000( 1 + 5/100 )^2`
= `8,000 xx 21/20 xx 21/20`
= Rs. 8,820
C.I. = A - P
= Rs. (8,820 - 8,000)
= Rs. 820
Now, C.I. - S.I. = Rs. ( 820 - 800 ) = Rs.
20.
Thus, the difference between the compound interest and the simple interest is Rs. 20.
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Solution
The correct option is A: Rs.3109
Given: Principal, P=Rs.8000
Rate, R =15%
Time =2 years 4 months =2+(412) years =213 years
Amount for 2 years is given as
Amount, A=P(1+R100)t [∵t=time]
= Rs. [8000×(1+15100)2]
=Rs.(8000 ×2320× 2320
=10580
Interest for 13 years is given as
I=P×R×t100
=10580×15×13100
=Rs.529
Total amount for 213 years =10580+529=Rs.11109.
∴ Compound Interest, C.I.= Toatal Amount - Principal =Rs.(11109 −8000)= Rs.3109.