Question:The difference between compound interest and simple on a sum for `2` years at `10%` per annum, when the interest is compounded annually is Rs.`16`. If the interest werw compound half yearly, the difference in two interests would be :
A `Rs. 24.81`
B `Rs. 31.61`
C `Rs. 32.40`
D `Rs. 2690`
+ ExplanationFor first year, S.I. = C.I.
Now, Rs.`16` is the S.I. on S.I. for `1` year .
:. Rs. `10` is S.I. on Rs.`100`
:. Rs. `16` is S.I. on Rs.`(100/10 xx 16)`
`= Rs. 160`
:. S.I. on principal for `1` year at `10%` is Rs. `160`
:. Principal `= Rs. ((100 xx 160)/(10 xx 1))`
`= Rs. 1600`
Amount for `2` years compounded half yearly
`= Rs. [1600 xx (1 + 5/100)^4]`
`= Rs. 1944.81`.
:. C.I.`= Rs. (1944.81 - 1600)`
`= Rs. 344.81`
S.I` = Rs. ((1600 xx 10 xx 2)/100)`
`= Rs. 320`.
:. (C.I) - (S.I)`= Rs. (344.81 - 320)`
`= Rs. 24.81`.
