SIMPLE INTEREST

SIMPLE INTEREST

SOME BASIC FORMULA E 

1) If P stands for Principal, R the rate per cent per annum. T the number of years, SI the simple interest and A the amount, then

Example:  On what sum of money lent out at 9% per annum simple interest for 6 years does the simple interest amount Rs 810?

Solution : 

                              

                               

2)

                    

  

                 

                                   

                                   

                             

Example:  A sum when reckoned at simple interest 2  1/2 % per annum amounts to Rs 630 after 2 years. Find the sum.

Solution :

                                   

                              

                                

SOME USEFUL SHORT-CUT METHODS

1) If a certain sum in T years at R% per annum amounts to Rs. A, then the sum will be

Example:   What principal will amount to Rs 864 at  8% per annum in 5  1/2 years?

Solution: 

                                         

                                         

                                          

                                          

2) The annual payment that will discharge a debt of Rs. A due in t years at r% per annum is

Example:   What annual payment will discharge a debt of Rs. 848 in 4 yrs at 4% per annum?

Solution:

                                                                

3) If a debt of Rs. M is paid in n number of installments and if the value of each instalments is Rs. a, then the borrowed (debt) amount is given by

Example:   What annual installment will discharge a debt of Rs. 4200 due in 5 years at 10% simple interest?

Solution: Here M = Rs. 4200, n = 5, y = 1, r = 10%, 

               a = annual installment = ?

                                      

                                               

4) If a certain sum of money becomes n times itself in T years at simple interest, then the rate of interest per annum is

Example: A certain sum of money becomes 8/5 of  itself in 5 years at a certain rate of interest. Find the rate per cent per annum 

Solution: 

                                 

  

                                 

                                        

5) If a certain sum of money becomes n times itself at R% per annum simple interest in T years, then

Example: A certain sum of money doubles itself in 7 yrs. In how many years will it become fourfold?

Solution:

                        

                         

                         

6) If a certain sum of money becomes n times itself in T years at a simple interest, then the time T in which it will become m times itself is given by

Example: A sum of money put out on simple interest doubles itself in 6   1/2 years. In how many years would it treble itself?

Solution: Here. n = 2,  m= 3. T = 13/2 years.

7) Effect of change of P, R and T on simple interest is given by the following formula :

    Change in Simple Interest   

=   Product of fixed parameter   X  difference of product of  

                      100                                 variable parameters

Example: If the interest on Rs. 1200 be more than the interest on Rs. 1000 by Rs. 50 in 3 years, the rate per cent is ?

Solution: Here change in SI = 50, P1 - P2 = 200, T = 3, R = ?

  8) If a certain sum is invested in n types of investments in such a manner that equal amount is obtained on each investment where interest rates are R1, R2,R3,........Rn respectively and time periods are T1, T2,T3........., Tn respectively, then the ratio in which the amounts are invested is

Example: A man invests an amount of Rs. 15860 in the names of his three sons A, B, C in  such a way that they get the same amount after 2, 3, and 4 years respectively. If the rate of simple interest is 5% then find the ratio in which the amount was invested for A, B and C?

Solution: From the above theorem

              

                           

                           

       

9) A sum of Rs X is lent out in n parts in such a way that the interest on first part at r1% for t1 yrs, the interest on second part at r2% for t2 yrs the interest on third part at r3% for t3 yrs, and so on, are equal the ratio i which the sum was divided in n parts is given by 

Example: A sum of Rs 2600 is lent out in two parts in such a way that the interest on one part at 10% for 5 yrs is equal to that on another part at 9% for 6 yrs. Find the two sums?

Solution: Ratio of one part to other part of Rs 2600

                            

                therefore 1st part : 2nd part 

                      

             

            

10) When there is a change in principal (P), Rate (R) and Time (T). then the value of simple interest I also changes and is given by

Example: If Rs. 85 amounts to Rs. 95 in 3 years, what Rs. 102 will amount to in 5 years at the same rate per cent?

Solution:  Here, P1= Rs. 85, A1= Rs. 95, T1 = 3 years.

                 P2 = Rs. 102, T2 = 5 years, R1 = R2 = R (say)

                                           

                                            

11) If a certain sum of money P lent out at SI amounts to A1 in T1 yrs and to A2 in T2 yrs, then

Example: A sum of money at simple interest amounts to Rs. 600 in 4 yrs and 650 in 6 yrs. Find the rate of interest per annum.

Solution: Here A1 = 600, T1 = 4, A2 = 650, T2 = 6