15. Mallapragada's Mathematics (Compound Interest-1)

Om Sri Ram                    Om Sri Ram                    Om Sri Ram
                                                                                 

COMPOUND INTEREST

Let Principal = P,   Rate = R%   Time = n years

1.  When interest in compound Annually:

Amount = P [1 + R/100]ⁿ

2.  When interest is compounded Half-yearly

Amount  = P[1+ (R/2)/100]²ⁿ

3.  When interest is compounded Quarterly:

Amount = P[ 1 + (r/4)/100]⁴ⁿ

4.  When interest is compounded Annually but time is in fraction, any 3 2/5 ears.   

Amount = P[1+R/100]³ x [1+(2/5R)/100]

5.  When Rates are different for different ears say R1%,R2%,R3%, for Ist,2^nd, and 3^rd ear respectively

Then Amount = P(1+R1/100)(1+R2/100)(1+R3/100)

6.  Present worth of Rs. X due n years hence is given by:

Present Worth = x/(1+R/100)ⁿ

1.  Find compound interest on Rs. 5000 at 4 % per annum for 2 years compounded annually

a)   5410  b)  5409   c) 5508   d) 5408


2.  Find compound interest on Rs. 6000 at 15% p.a for 2 years 4 months compound annually.

a)  8333  B) 8332    c)8334   d)8000

3. Find the compound inerest on Rs. 10,000 in 2 ears at 4% per annum the interest being compounded half-yearly.

(a)  10824   (b) 10825 ( c)10826  (d)10827 


4. Find the compound interest on Rs. 16000 at 20% per annum for 9 months, compound  Quarterly.    

(a) 18522   (b)18533 ( c)18534  (d) 18523



5. If the simple interest on a sum of money at 5% per annum for 3 ears is Rs. 1200, fi9nd the compound interest on the same sum for the same period at the same rate.

(a) 9260  (b) Rs. 9261  ( c)9262  (d) 9263



6. Rama invested Rs. 15,000 @ 10% per annum for one ear.  Of the interest is compounded half-ear, then the amount received b Ram. at the end of the ear will be:

(a) 16000  (b)  16538  ( c) 16537.50 (d) 16539


7. A man save Rs. 200 at the end of each ear and lends the money at 5% compound interest.  How much will it become at the end of 3 years?

(a) 662.02   (b) 662  ( c)663   (d)662.50


8. The compound interest on Rs. 20,480 at 6 1/4% per annum for 2 years 73 days is

(a) 2930  (b) 2929    ( c)2931  (d) 2915


9. What will be the compound interest on a sum of Rs. 20000 after 3 years at the rate of 12 p.c.p.a.?

(a) 8098.56     (b) 9008  ( c) 8098   (d) 8099

10. Rama invested an amount of Rs./ 8000 in a fixed deposit scheme for 2 ears at compound interest rate 5 p.c.p.a. How much amount will Ram get on maturity of the fixed deposit? 

a)8820 b)8810   c)  8815  d) 8825 

1.  Find compound interest on Rs. 5000 at 4 % per annum for 2 years compounded annually

Ans.Amount = P(1+R/100)ⁿ
                             = 5000(1+4/100)² 
                   = 5000x26/25 x26/25 = Rs. 5408.


2.  Find compound interest on Rs. 6000 at 15% p.a for 2 years 4 months compound annually.

Sol. Time = 2.4/12 months, P=6000 R. 15%
         A.= {6000x(1+15/100)² x [1+(15 x 1/3)/100]}
              = [6000x 23/20 x23/20 x 21/20]
              =  (3 x 23x23x21)/4  = 8331.75
              =Rounded  Rs. 8332
        C.I = A-P = 8332-6000 =2332
     
3. Find the compound interest on Rs. 10,000 in 2 years at 4% per annum the interest being compounded half-yearly.

 Sol. P. = 10,000  N = 2  R= 4%
         A = P[(1+(R/2)/100]²ⁿ  = 10000[(1+4/2/100)²ⁿ
             = 10000(1+2/100)²ⁿ  = 10000(51/50)^2x2
             = 10000x 51/50x51/50x51/50x51/50
             = 10824.32  = Rounded Ans. 10824          


4. Find the compound interest on Rs. 16000 at 20% per annum for 9 months, compound  Quarterly.    
Sol. P=16000 R=20% Per annum =5% per quarter          T= 9 months = 3 quarters
        A = P(1+R/100)³  = 16000(1 + 20/100)³
        A = 16000(1+5/100)³ = 16000x21/20x21/20x21/20
            =18522
 
5. If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, fiend the compound interest on the same sum for the same period at the same rate.

Sol.  S.I = 1200  Rate 5% Time = 3 years
         I = PTR/100 =
       1200 = (P x 3 x 5)/ 100
.           P = 1200 x 100/3 x 5 = Rs. 8000
         A = [8000(1+5/100)³] = 8000x21/20x21/20x21/20
             = Rs. 9261

6. Rama invested Rs. 15,000 @ 10% per annum for one ear.  Of the interest is compounded half-ear, then the amount received  Ram. at the end of the ear will be:

Sol. P = Rs. 15,000   R= 10%  p.a. = 5% per half year 
       T = 1 year = = 2 half – years.
       A = [15000 x (1+5/200)]² = 15000x21/20x21/20
           = (150x 21 x 21)/(2x2) = 16537.50       


7. A man save Rs. 200 at the end of each ear and lends the money at 5% compound interest.  How much will it become at the end of 3 years?
Sol. A = 200(1+5/100)³ + 200(1+5/100)² +200(1+5/100) 
        A = 200x21/20x21/20x21/20+200x21/20x21/20 +
                200x21/20 
               = 200x21/20{21/20x21/20+21/20 +1}
               = 662.02


8. The compound interest on Rs. 20,480 at 6 1/4% per annum for 2 years 73 days is
Sol. P = 20,480   R=61/4% = 25/4% , T= 2x73/365=21/5
        A= Rs. [20480x(1+25/4x100)²][1+(1/5x25/4)100]
           =Rs. {20480 x 17/16 x 17/6 x 81/80}=23409
       C.I = 23409-20480=Rs. 2929
       

9. What will be the compound interest on a sum of Rs. 20000 after 3 years at the rate of 12 p.c.p.a.?
Sol. A = [20000x(1+12/100)³]
           = 20000x28/25 x28/25 x28/25
           = 28098.56
     C.I = 28098.56-20000 = 8098.56

10. Rama invested an amount of Rs./ 8000 in a fixed deposit scheme for 2 ears at compound interest rate 5 p.c.p.a. How much amount will Ram get on maturity of the fixed deposit? 

Amount = Rs. [8000x(1+5/100)²

                =Rs. 8000x21/20x21/20 = 8820