Simple Interest and Compound Interest - Concepts, Tricks and Formulas

Simple and Compound Interest

What is S.I (Simple Interest) and C.I (Compound Interest)? In this post we will learn how to calculate simple interest and compound interest on certain money or principal lent or borrowed. What is the difference between simple interest and compound interest? After going through this post you will understand everything like principal, amount, interest, Rate, installments etc.

INTEREST

Interest is the payment from a borrower to a lender above repayment of amount borrowed (principal) at a particular rate. It is the difference between principal and amount.

There are two types of interest:
 1.  Simple Interest: It is the interest calculated on the principal amount only for any period of time.

 2.  Compound Interest: It is the interest calculated together on the principal amount and interest of the previous period of time. In other word it is same as simple interest except it includes interest on interest for successive years. It means if for first year principal is P and interest is I, then for the next year principal will be (P + I).

TERMINOLOGY

 1.  Principal or Sum: Principal is the money lent by the lender or money borrow by the borrower.

 2.  Amount: It is equal to the sum of the principal and interest.

 3.  Rate: It is equal to particular rupees for every 100 rupees of the money lent for a particular period of time.

 4.  Time: It is the period for which amount borrow by the borrower. Interest is usually paid yearly (per annum), half-yearly (per 6 months), quarterly (per 4 months) or daily.

 METHODS 

To find Simple Interest

 1.  Direct Formula: S.I. = (P x R x T)/100
Here S.I = Simple Interest; P = Principal; R = Rate of interest; T = Time period (in years)

 2.  Method of Percentage: We always take Principal as 100% and Rate as (R x T)%

Example: A sum of Rs 40000 is lent for 5 years at the rate of 15% per annum. Find interest.
Solution: Rate of interest = 5 x 15% = 75%
   ⇒ Simple Interest = 40000 x 75/100 = Rs 30000

Installment at Simple Interest

Annual installment that will discharge a debt of Rs 'Z' due in 'N' years at R% simple interest will be: Let I be the annual installment.
[I + (I x R x (N-1))/100]  +  [I + (I x R x (N-2))/100]  + …. +  [I + (I x R x (N-N))/100]  = Z 

To find Compound Interest

 1.  Direct Formula: C.I. = P(1 + R/100)n – P

Here C.I = Compound Interest; P = Principal; R = Rate of interest; n = Time period

• When interest is compounded Half-yearly: Time = 2n; Rate = R/2

• When interest is compounded Quarterly: Time = 4n; Rate = R/4

• When interest is compounded Monthly: Time = 12n; Rate = R/12

• When interest is compounded Daily: Time = 365n; Rate = R/365

 2.  Method of percentage: We always take Principal as 100%.

• Rate for one year will be = R%

• Rate for two years will be = 2R + R2/100

• Rate for three years will be = 3R + 3R2/100 + R3/10000

Example: Find the C.I on Rs 10000 at 10% per annum for 2 years.
Solution: Rate of Interest = 2 x 10 + 102/100 = 21%
   ⇒ Compound Interest = 10000 x 21/100 = Rs 2100

 3.  Blocks method: This method is based on the fact that S.I & C.I remains same for first year. For second year, C.I will include interest on interest of first year and so on.

Example: Find the C.I on Rs 1200 at 10% per annum for 3 years compounded annually.
Solution:

We can write this block diagram theoretically like this:

• Rule to find C.I for 3 years: ‘331’
  First ‘3’ means multiply first interest on principal by '3'.
  Second ‘3’ means multiply interest on first interest by '3'.
  ‘1’ means multiply interest on second interest by '1'.

S.I on principal = 1200 x 10/100 = Rs 120
   ⇒ Multiply it by 3, we get = 120 x 3 = Rs 360

Now, S.I on this interest = 120  x 10/100 = Rs 12
   ⇒ Multiply it by 3, we get = 12 x 3 = Rs 36

At last, S.I on this interest = 12 x 10/10 = Rs 1.2
   ⇒ Total interest = 360 + 36 + 1.2 = Rs 397.20

• Rule to find C.I for 2 years: ‘21’

• Rule to find C.I for 4 years: ‘4641’

Installment at Compound Interest

 1.  Annual installment that will discharge a debt of Rs 'Z' due in 'n' years at R% compound interest will be: Let I be installment per year.

Second formula: 

 2.  Present worth (Pn) =  Installment/(1+ R/100)n
For First year n = 1; for second year n = 2 and so on. 

Sum of present worths of all years (P1 + P2 +...+ Pn) = Total debt or amount lent or borrowed.

Relation between S.I and C.I

 1.  If S.I on certain sum for two years is x and C.I is y, then: y = x(1+ R/200)
 2.  For Two years: Principal = Difference in C.I & S.I x (100/R)2
 3.  For Two years: Principal = (1st year S.I)2/Difference between C.I & S.I
 4.  For Two years: Rate = [2 x Difference in C.I & S.I x 100]/S.I
 5.  For three years: Difference between C.I & S.I = PR2(300 + R)/(100)3

These are few tricks to solve S.I and C.I problems. After understanding above methods you will be able to solve simple interest and compound interest problems easily. This chapter is also useful in our day-to-day life as it is connected with us. For example Banks provide us compound interest and we can calculate now. Those who take loan or lent money can calculate easily the amount of installments. Will provide more methods in next post which will be problem specific. Good Luck 👍