Compound Interest Set 2:

1. The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 350. What is definitely the rate of interest per cent per annum?
   A.9,300
   B.7600
   C.12000
   D.Data inadequate
   E.None of these
   
   Answer – D.Data inadequate
   Explanation :
   Difference = Pr2/(100)2
   = (350×100×100)/(P×r2)
   P is not given
   
   
   
2. Aswin invested an amount of Rs.9000 in a fixed deposit scheme for 2 years at CI rate 6% pa. How much amount will Aswin get on maturity of the fixed amount ?
   A.Rs.11,230
   B.Rs.10,250
   C.Rs.10,112
   D.Data inadequate
   E.None of these
   
   Answer – C.Rs.10,112
   Explanation :
   Amount = 9000*106/100*106/100
   = 9000*53/50*53/50
   = 10,112
   
   
   
3. A sum of money invested for 7years in Scheme 1 which offers SI at a rate of 8% pa. The amount received from Scheme 1 after 7 years invested for 2 years in Scheme 2 which offers CI rate of 10% pa. If the interest received from Scheme B was Rs.1638. What was the sum invested in Scheme 1 ?
   A.Rs.7500
   B.Rs.5000
   C.Rs.8200
   D.Rs.9000
   E.None of these
   
   Answer – B.Rs.5000
   Explanation :
   SI =>Amount = x*8*7/100 + x = 56x+100x/100 = 156x/100 = 39x/25
   CI=> 39x/25[(1+10/100)2 – 1]
   1638 = 39x/25[121/100 – 1] = 39x/100[21/100]
   X = 1638*100*25/21*39 = 5000
   
   
   
4. Rs.5200 was partly invested in Scheme A at 10% pa CI for 2 years and Partly invested in Scheme B at 10% pa SI for 4 years. Both the schemes earn equal interests. How much was invested in Scheme A ?
   A.Rs.1790
   B.Rs.2200
   C.Rs.3410
   D.Rs.2670
   E.None of these
   
   Answer – C.Rs.3410
   Explanation :
   Amount invested in Scheme B = X
   Amount invested in Scheme A = 5200 – x
   X*10*4/100 = (5200-x)*21/100……………………[(1-10/100)2-1] = 21/100
   40x/100 = (5200-x)*21/100
   2x/5 = (5200-x)*21/100
   200x = 5200*21*5 – x*5*21
   200x = 546000 – 105x
   305x = 546000
   X = 1790
   Scheme A = 5200 – 1790 = 3410
   
   
   
5. The CI on Rs.7000 for 3 years at 5% for first year, 7% for second year, 10% for the third year will be
   A.Rs.1800
   B.Rs.1530
   C.Rs.1651
   D.Rs.2050
   E.None of these
   
   Answer – C.Rs.1651
   Explanation :
   A = 7000*105/100*107/100*110/100
   = 7000*1.05*1.07*1.1
   = 8650.95 = 8651
   CI = 8651-7000 = 1651
   
   
   
6. Poorni and Priyanka have to clear their respective loans by paying 2 equal annual instalments of Rs.20000 each. Poorni pays at 10% pa of SI and Priyanka pays at 10% CI pa. What is the difference in their payments ?
   A.200
   B.300
   C.400
   D.500
   E.None of these
   
   Answer – A.200
   Explanation :
   D =[(20,000 *110/100*110/100) – 20,000]  – 20,000 *10*2/100
   =[ 24200-20000]-4000
   =4200 – 4000
   D = 200
   
   
   
7. A sum of Rs.3,50,500 is to be paid back in 2 equal annual instalments. How much is each instalment, if the rate of interest charged 4% per annum compound annually ?
   A.Rs.1,90,450
   B.Rs.1,65,876
   C.Rs.1,76,545
   D.Rs.1,85,834
   E.None of these
   
   Answer – D.Rs.1,85,834
   Explanation :
   Total value of all the 3 instalments
   [X*100/104] + [X*100*100/104]  = 3,50,500
   X*25/26 + x*625/676 = 3,50,500
   X*25/26[1+25/26] = 3,50,500
   X*25/26[51/26] = 3,50,500
   X = 3,50,500*676/25*51 = 1,85,833.72 = 1,85,834
   
   
   
8. At CI, if a certain sum of money is doubled in 4 years, then the amount will be four fold in how many years ?
   A.7years
   B.4years
   C.10years
   D.8years
   E.None of these
   
   Answer – D.8years
   Explanation : 2n = 2*4 = 8 years
   
   
   
9. X has lent some money to A at 5% pa and B at 8% pa. At the end of the year he has gain the overall interest at 7% pa.In what ratio has he lent the money to A and B ?
   A.2:1
   B.1:2
   C.3:1
   D.1:4
   E.None of these
   
   Answer – B.1:2
   Explanation :
   5………………………….8
   ……………7…………….
   1………………………….2
   Ratio A : B = 1:2
   
   
   
10. The difference between interest received by X and Y is Rs.315 on Rs.3500 for 3 years. What is the difference in rate of interest ?
    A.1.5%
    B.2%
    C.3%
    D.2.7%
    E.None of these
    
    Answer – C.3%
    Explanation :
    3500*3/100(R1-R2) = 315
    R1-R2 = 315*100/10500 = 3%