Simple Interest and Compound Interest

 SIMPLE INTEREST (SI)

Principal(P):- The money borrowed or lent out for a certain period is called Principal or Sum.

Time Period (T):- Total time taken in year 

Rate of interest(R):- Rate on Principal value w.r.t time period per annum 

Simple Interest(SI) :- Extra money paid on Principal.

SI is same for all the years.

Amount(A):- Principal  + SI , so A = P + SI

Basic formula:-

SI = PTR/100 

• If T is given in months, it has to be converted in years, so the period in months has to be divided by 12.

• The day on which money is deposited is not counted,  while the day on which money is withdrawn is counted. 

• Keep Principal (P) is always 100 and calculate accordingly. 

👉 Effective Rate = (Amount  - Sum) %                                                       = (A - P )%

👉 72 rule - 

               Given number of years for the money to double = 72/(annual rate of interest) = 72/r% 

Example :
1. Find S.I on Rs.12000/- at rate of 5% per annum for 10 yrs?
Solution:
       100 Principal = (5 × 10) = 50 SI
       12000 Principal = 50/100 × 12000 = Rs.6000

2. If a certain sum amounts to Rs.52000 at 6% p.a in 5 yrs at S.I. Find the sum?
Solution:
        100 Principal = 6 × 5 = 30 SI
         A = 100 + 30 = 130
         130 A = 100 Sum
       52000 A = 40000

3. If a certain sum doubles itself in 12 yrs at S.I, then it will be 4times how many years?
Solution:
         P               A            SI
       100            200         200 - 100 = 100
       100            400         300
    (P - constant)
       100 SI = 12 yrs
       300 SI = 12 × 3 = 36 yrs

4. If a certain sum triple itself in 25 yrs at SI, find rate of interest p.a?
Solution:
             P            A         SI
           100         300     200
 In 25 yrs, SI = 200
So, in 1 Yr SI = 200/25 = 8% 
(200 SI = 25 × r, then r = 8%)

5. If a certain sum double itself at 12.5% p.a at SI. Find time period?
Solution:
            P        A         SI
          100      200      100
So, 100 = 12.5 × T ; then T = 8 Yr

6. The SI of a certain sum of money for 1st 2yr, r =3%, for the next 3yr, r=4% p.a. and for the period beyond 5yr, r = 6% respectively. If the total interest in 8yr is Rs.720. Find the sum?
Solution:
              2yr             3yr                   >5yr
              3%             4%                  6%
SI = 2 × 3=6       3 × 4 = 12       (8 - 5) × 6 = 18
Total SI = 6 + 12 + 18 = 36
When SI value 36 = 100 Sum
So, SI value 720 = 100/36 × 720 = Rs.2000

7. 

COMPOUND INTEREST (CI)

After a specified period, the difference between the amount and the money borrowed is called Compound Interest (CI) for that period. 

• In such cases, the amount after first unit of time becomes the principal for the second unit, the amount after second unit becomes the principal for the third unit and so on.

Tricks for finding r%

1. For 2 yr, r% = √(A/P) × 100 - 100

2. For 3 yr, r% = ∛(A/P) × 100 - 100

3. For n yr, r% = (A/P)¹/ⁿ × 100 - 100

Example :

1. If SI on a certain amount in 2yrs at 6% p.a is Rs.2400. Find C.I on the same sum at same rate and same time?

Solution:

    SI for 2yrs  → i. 1st yr;  SI = 1200

                            ii. 2nd yr; SI = 1200 (SI is same for all years)

    CI for 2yrs → i. 1st yr;  CI = 1200

                           ii. 2nd yr; CI = 1200 + 1200 × 6% = 1272

     So, CI = 1200 + 1272 = Rs.2472

2. If Rs.40,000 amounts to Rs.48400 are 10% p.a at CI, find time period?

Solution:

           P                        A

       40000                48400

   Divided by 4, in both P & A

          100                  121

          (10)²                (11)²

  Here r = 10% and its power is 2. So, t = n = time period = 2 years

3. If the difference between CI & SI on a certain sum of money in 2 yrs at the rate of 8% p.a is 256. Find the sum?

Solution:

Sum(P)         SI           CI

100                8             8  -   1st yr

                      8        8 + 8 × 8/100 = 8.64   - 2nd yr

Total SI = 16  and CI = 16.64

Given, difference (CI - SI) = 0.64, then sum is 100

When difference is 256, then sum = (100/0.64) × 256 = Rs.40,000.

4. If Rs.24,000 to Rs.27,783 in 3 yrs at CI. Find rate of interest p.a.

Solution:

     P                    A

  24000           27783

Divided by 3 in both P & A

= 8000             9261 - after 3 yrs

But, for 1 Yr., 

(8000)¹/³ = 20              (9261)¹/³ = 21

For 20 = 1 part

100 = 5 part = 5% = r %

Do it yourself 

1. Three sums Rs. x, Rs. 648 and Rs. 729 are such that Rs. 648 is the simple interest on Rs. x and Rs. 729 is the simple interest on Rs. 648. If in all the three cases, rate of interest per annum and the time for which interest is calculated is the same, then find the value of x (in Rs.)? (Ans.Rs.576)

2. A sum of money becomes 5 times itself in 5 yrs in a certain rate of simple interest in how many years will it become 7 times itself at the same rate of interest? (Ans. 7.5 yrs)

Previous Years Questions 

1. Find the difference between the compound interest & simple interest for the sum of Rs.1500 at 10% p.a for 2 years? (Ans. 15)

2. In what time Rs.1500 will become Rs.1815 at the rate of S.I of 7% p.a.? (Ans. 3 years)

3. Rate of interest remaining same, the difference between CI & SI generated in two years on an investment of Rs.10,000 amounts to Rs.64. Determine the rate of  interest per annum?

4. If the ratio of principal and the SI of 5 years is 10 : 3, then the rate of interest is : (Ans. 6%)

5. On lending a certain sum of money on compound interest, one gets Rs.9050 in 2 years and Rs.9500 in 3 years. What is the rate of interest (approximately) ?