If the compound interest on a sum of rs.8000 for 2 years is rs.1680 then the rate of interest is

1. The simple Interest on a certain sum of money at the rate of 4% p.a.  for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ?
a) 5%
b)6%  
c)7%  
d)8%

2. The interest on a certain deposit at 4.5% p.a. is Rs. 405 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ?
a)Rs.50          
b) Rs. 45        
c)Rs.40.5      
d)Rs. 48.5

3. Mr.Govind invested an amount of Rs.13900  divided in two different schemes S1 and S2 at the simple interst rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in two years was Rs.3508, what was the amount invested in Scheme S2?
a) Rs.6400    
b)Rs.6500      
c) Rs.7200    
d) Rs.7500

4. A sum of money was invested in a bank at 8%  simple interest p.a. for 3 years. Instead had it been invested in mutual fund at 8.5% p.a. simple interest for 4 years, the earning would have been Rs.500 more. What is the sum invested?
a) Rs.4500                
b) Rs.5000                
c) Rs.3500                
d) Rs. 5500

5. A person borrowed Rs.600 @ 3% per annum  S.I and Rs.800 @ 4½ % per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.246. The number of years, after which the borrowed sum is to be returned, is
a) 2 years      
b) 3years      
 c) 4 years      
d) 5 years

6. A sum of Rs.13000 is divided into three parts such that the simple interests accrued on them for two, three and four years respectively may be equal. Find the amount deposited for 4 years.
a)5000
b) 6000        
c)4000          
d)3000

7. A sum of Rs.100 is lent at simple interest of 3% p.a. for the first month, 9% p.a. for the second month, 27% p.a. for the third month and so on. What is the total amount of interest earned at the end of the year approximately
a) Rs.797160
b) Rs.791160
 c)Rs.65930    
d) Rs.66430

8. If the simple interest on a sum of money at twelve percent per annum for two years is Rs.3800, compound interest on the same sum for the same period at the same rate of interest is
a) Rs.4028    
b)Rs.4100      
c)Rs.4128      
d) 4228

9. A sum of money is borrowed and paid back in two annual installments of Rs.882 each allowing 5% compound interest. The sum borrowed was :
a) Rs.1620    
b) Rs. 1640    
c)Rs.1680
d)Rs.1700

10. Rakesh invested an amount of Rs.12000 at the rate of 10% simple interest and another amount at the rate of 20% simple interest. The total interest earned at the end of one year on the amount invested became 14 p.c.p.a. Find the total amount invested .
a) Rs.20000      
b)Rs.22000    
c) Rs.24000  
d) Rs.25000

11.The rate fo simple interest in two banks is in the ratio of 4 : 5 . Amith wants to deposit his total saving in these two banks  in such a way that he should receive equal half yearly interest from both. He should deposits the saving in the banks in the ratio of:
a)  2 : 5  
b)5 : 4
c)  5 : 3          
d)4 : 5

12. A sum of money becomes triple itself in 16 years. In how many years will it become 5 times at the same rate?
a) 32
b) 15  
c) 27
d) 30

13. The compound interest on Rs.30,000 at 7% per annum is Rs. 4347. The period (in years) is:
a) 2    
b) 2 ½            
c) 3                
d) 4

14. At what rate of compound interest per annum will a sum of Rs.1200 become Rs.1348.32 in 2 years?
a) 6%
b) 6.5%          
c)7%  
d) 7.5%

15. If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time?
a)Rs. 52        
b)Rs. 51.25    
c)Rs. 54.25    
d) Rs. 60

Answers 

1.(a)  S.I. = 1680, R = 4%  T = 5 years
    Principal = (100 *1680)/ (5*4) = 8400
    So P = 8400
    Rate = (100 *1680)/ (8400 * 4) = 5%

2. (b) S.I. = Rs. 405 R = 4.5% T = 1 year
   Principal = (100 *405)/(4.5*1) =  Rs.9000
   S.I at 5% interest = (9000*5*1)/100 = Rs.450
   Difference in interest = 450 – 405 = Rs.45

3. (a) Let the sum invested in Scheme S1 be Rs.x and that in Scheme S2 be Rs.(13900-x).
    Then, (x*14*2)/100 + ((13900-x)*11*2)/100 = 3508;
    28x-22x= 3350800-(13900*22);
    6x = 45000;    x= 7500
    So sum invested in Scheme S2 = Rs. (13900-7500) = Rs.6400
4. (b) Let the sum be Rs.x
   S.I from the bank = x*8*3/100 = 34x/100Earnings in the form of interest from mutual fund  = (x * 8.5
   *4)/100 = 34x/100
   Given that 34x/100 – 34x/100  = Rs.500 ; x = 5000
   : . The sum invested = 5000
5.(c)  Let the time be x years. Then (600 *3* x)/100 + (800*9*x)/(2*100) = 24
   18x+ 36x = 246 ;   x = 246/54 = 4 years
   Required time = 4 years
6. (b) Let the amounts be x, y, z in ascending order of value. As the interest rate and interest             accrued are same for 4 years 3 years and 2 years i.e. 4x = 3y = 2z  = k.
    L.C.M. of 4,3,2 = 12 So x:y:z: = 3000 : 4000 :6000
    The amount deposited for 4 years = 3000
7.(d)  Total amount of Interest  is
    I = P/100 * 1[3/12 + 9/12 +27/12…. 312/12
    Where P = 100;  I = 1/12 (3+9+…..312)
    I = 1/12(3(312-1))/3-1
    = 531440* 3/12*2 =Rs.66430
8. (a)  S I for 2 years = 3800 ie for one year =1900
    The compound interest for Rs.1900 for the second year = 1900*12/100 =228
    The CI for two years  3800+228 = 4028
9. (b)  Principal = 882/(1+(5/100)) + 882/(1+(5/100)= (882*20)/21+ (882*400)/441
                =840 +800 = Rs.1640
10. (a). Let the second amount be Rs.x. then,
(12000* 10 * 1)/100 + (x*20 *1)/100 = ((12000 +x)* 14*1)/100
                = 1200 +x/5 = (168000 +14x)/100
600000 + 100x = 840000 +70 x
30x = 240000;  X = 8000
     Total investment = 12000 +8000 = Rs.20000
11.  (b)
12. (a) Let sum be Rs.100. After 16 years it become 300. With in 16 years it increased Rs.200 i.e. after 8 years it is doubled. So after 32 years interest become Rs.400. Total Rs.500 i.e. 5 times more than the
    sum. So 32 years is the answer.
13. (a) Amount = Rs. (30000 + 4347) = Rs. 34347.
     Let the time be n years.
     Then, 30000 (1 + 7/100)n = 34347
     (107/100) n = 34347/30000 = 11449/10000 = (107/100)2
     So the period is 2 years.
14. (a) Let the rate be R% p.a. (1+ R )2 = 1348.32. Then, 1200* (1+ (R/100))2 = 1348.32
     (1+R/100)2 = 134832/120000 = 11236/10000 :. (1 + R/100) 2 = (106/100)2
     1 + R/100 = 106/100.  So R = 6%
15. (b)  Simple interest for 2 years = Rs.50 ie. For 1 years Rs. 25. . In the first year the S.I and C.I are
     same ie.Rs. 25. So in  the 2nd year  in C.I calculated for 1 years interest also. So in second years for

     Rs.25 interest is 25*5/100 = 1.25 . So total C.P = 51.25.

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