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Deducing a Formula for Compound Interest

At the end of the first year,

P × R T
×
SI = 1 100
1
P × R 1  R 
×
A = P + 1 100 = P 1 + 100  = P 2 (Q T = 1)
1 
1
1

At the end of the 2nd year,
×
P × R T  R  R
SI = 2 = P 1 +  × (Q T = 1)
1 
2
100  100 100
 R   R   R 
A = P + SI = P 1 + 100  + P 1 + 100  100 
 
1 
1 
2
2
2




R 
R  
R 
= P 1 + 100  1 + 100 = P 1 + 100 2

 
1 

1 


Proceeding in this way, the amount at the end of n years will be
 R  n
A = P 1 + 100
1 

n

Rate of interest (in %)
R 

or A = P 1 + 100 n Time (Conversion periods) ...(i)



Principal
The above formula gives the “Amount” at compound interest.
Compound interest (CI) = A – P
n
R 


R 
,
⇒ CI = P 1 + 100  n − P     Here A = P 1 + 100     





  R  n 
∴ CI = P   1 +  − 1
   100  
maths fun
Take any value for the principal, rate of interest, and time period.
For your reference, let P = `1000, T = 5 years and R = 5% p.a. compounded annually.
Compute the Simple Interest (SI) and the Compound Interest (CI) and make a table for the data.
Time Period (years) SI (in `) CI (in `) 300 Y SI Scale: Y-axis: 1 unit = `25
1 50 50 275
250 CI
2 100 103 225
200
3 175
4 150
125
5 Interest (in `) 100
75
Draw a double bar graph to compare the simple interest and 50
25
the compound interest visually. 1 year 2 years 3 years 4 years 5 years X
Discuss what you observe in the class. Ti me (in years)
181 Comparing Quantities