Compound Interest
 

  1. Question: The compound interest on a sum for `2` years is Rs.`832` and the simple interest on the same sum for the same period is Rs.`800`. The difference between the compound interest and the simple interest for `3` years will be :

    A
    `Rs. 48`

    B
    `Rs. 66.56`

    C
    `Rs. 98.56`

    D
    none of these

    Note: Diff. in C.I. & S.I.for `2` years `= Rs. 32` S.I. for `1` years`= Rs.400`. :. S.I. on Rs.`400` for `1` year`= Rs.32` :. Rate `= ((100 xx 32)/(400 xx 1))%` `= 8%` Hence, diff. in C.I. and S.I. for `3rd` year = S.I.on Rs.`832` `= Rs. (832 xx 8/100 xx 1)` `= Rs. 66.56`.
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  2. 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`

    Note: For 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`.
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  3. Question: A sum of money becomes Rs. `13380` after `3`years and Rs. Rs. `20070` after `6` years on compound interest .The sum is :

    A
    `Rs. 8800`

    B
    `Rs. 8890`

    C
    `Rs. 8920`

    D
    `Rs. 9040`

    Note: Let the sum be x. Then, `x(1 + R/100)^3` `= 13380 & x (1 + R/100)^6` `= 20070` On diiving, we get `(1 + R/100)^3` `= 20070/13380` `= 3/2` `:. x xx 3/2 = 13380 ⇒ x` `= (13380 xx 2/3)` `= 8920`. Hence, the sum is Rs.`8920`.
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  4. Question: A loan was repaid in two annual instalments of Rs. `121` each. If the rate of interest be `10%` per annum, compunded annuallly, the sum borrowed was :

    A
    `Rs. 200`

    B
    `Rs. 210`

    C
    `Rs. 217.80`

    D
    `Rs. 216`

    Note: Principal = ( P.W. of Rs. `121` due `1` year hence) + (P.W. of Rs.`121` due `2` years hence) `= [121/((1 + 10/100)) + 121/(1 + 10/100)^2]` `= Rs. 210`
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  5. Question: A sum of Rs.`1100` was taken as a loan. This is to be repaid in two equal instalments. If the rate of interest be `20%`compouonded annually, then the value of each instalment is :

    A
    `Rs. 842`

    B
    `Rs. 792`

    C
    `Rs. 720`

    D
    `Rs. 700`

    Note: Let the value of each instalment be Rs.x Then, (p.w. of Rs. x. due `1` year hence) + (p.w. of Rs.x due `2` years hence) `= Rs. 1100`. `:. x/((1 + 20/100)) + x/((1 + 20/100))^2` `= 100` `or (5x)/6 + (25x)/36` `= 1100` `or 55x = 36 xx 1100` `:. x = ((36 xx 1100)/55)` ` = Rs. 720`
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  6. Question: A man borrows Rs. `12500` from a bank at `20%` compound interest. At the end of every year he pays Rs.`2000` as part repayment. How much does he still owe to the bank after three such instalments ?

    A
    `Rs. 15600`

    B
    `Rs. 12864`

    C
    `Rs. 12000`

    D
    none of these

    Note: Balabce`= Rs.[12500 xx (1 + 20/100)^3]` `=Rs.[2000 xx (1 + 20/100)^2 + 2000 xx (1 + 20/100) + 2000]` `= Rs. [(12500 xx 6/5 xx 6/5 xx 6/5)] - [(2000 xx 6/5 xx 6/5 + 2000 xx 6/5 + 2000)]` `= Rs. [21600 - (2880 + 2400 + 2000)]` `= Rs. 14320`
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  7. Question: The difference between simple interest and compound interest on Rs.`1200` for one year at `10%` per annum, reckoned half - yearly is :

    A
    Nill

    B
    `Rs. 13.20`

    C
    `Rs. 8.80`

    D
    `Rs. 3`

    Note: S.I.`= Rs. ((1200 xx 10 xx 1)/100)` `= Rs. 120`. C.I.`= Rs.[1200 xx (1 + 5/100)^2 - 1200]` `= Rs. 123` :. (C.I.) - (S.I.)`= Rs. (123 - 120)` `= Rs. 3`.
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  8. Question: The difference between the compound interests on Rs.`1600` for one year at `20%`per annum, when compounded half yearly and quarterly is :

    A
    `Rs. 8.81`

    B
    `Rs. 9.4`

    C
    `Rs. 10.36`

    D
    `Rs. 8.50`

    Note: C.I. when interest is compounded half yearly = Rs.`[1600 xx (1 + 10/100)^2 - 1600]` `= Rs. 336` C.I. when interest is compounded quarterly = Rs.`[1600 xx (1 + 5/100)^4 - 1600]` `= Rs. 344.81` :. Difference = Rs.`(344.81 - 336)` `= Rs. 8.81`.
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  9. Question: The compound interest on Rs.`8000` at `15%` per annum for `2` years `4` months, compounded annually is :

    A
    `Rs. 2980`

    B
    `Rs. 3091`

    C
    `Rs. 3109`

    D
    `Rs. 3100`

    Note: Time`= 2` years `4`months`= 2 4/12` years `= 2 1/3`years. :. C.I.`= Rs.[8000 xx (1 + 15/100)^2 xx (1 + (1/3 xx 15)/100) - 8000]` = Rs.` (8000 xx 23/ 20 xx 23/20 xx 21/20 - 8000)` `= Rs. 3109`.
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  10. Question: The present worth of Rs.`4913` due `3` years hence at years hence at `6 1/4%`per annum compound interest is :

    A
    `Rs. 4216`

    B
    `Rs. 4096`

    C
    `Rs. 4200`

    D
    `Rs. 4168%`

    Note: P.W.`= 4813/(1 + 25/(4 xx 100)^3` `= (4813 xx 16/17 xx 16/17 xx 16/17)` `= Rs. 4096`
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