FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.11- The simple interest on
300 at the rate of 4% p.a. with that on500 at the rate of 3% p.a. both for the
same period, is ` 162. Find the time period. [Ans. 6 years] - Calculate the interest on
10,000 for 10 years at 10% p.a. [Ans.10,000]
1.2.2 COMPOUND INTEREST
Interest as soon as it is due after a certain period, is added to the principal and the interest for the succeeding
period is based upon the principal and interest added together. Hence the principal does not remain
same, but increases at the end of each interest period.
A year is generally taken as the interest-period, but in most cases it may be half-year or quarter-year.
Note. Compound interest is calculated by deducting the principal from the amount (principal + interest) at
the end of the given period.
Simple Interest for 3 years on an amount was 3000 and compound interest on the same amount at the same rate of interest for 2 years was 2, 100. Find the principal and the rate in interest.
Let the amount be x and rate of interest = x i. Now x. i. 3. = 3000 ... (i) Again x (1 + i)^2 – x = 2100, from C.I = P (1 + i)^2 – P, P = Principal or, xi (2 + i) = 2100 or, 1000 (2 + i) = 2100, by (i) or, (2 + i) = 2.1 or, i = 2.1 – 2 = 0.1 = 10% From x. (0. 1). 3 = 3000 or, x = 10,000 ∴ Required principal is 10,000 and rate of interest is 10%
Using Logarithm :
In calculating compound interest for a large number of years, arithmetical calculation becomes too big
and out of control. Hence by applying logarithm to the formula of compound interest, the solution becomes
easy.
Symbols :
Let P be the Principal (original)
A be the amount
i be the Interest on Re. 1 for 1 year
n be the Number of years (interest period).
Formula : A = P(1 + i)n .... (i)
Cor.1. In formula (i) since P amount to A in years, P may be said to be present value of the sum A due in n
years.
( )
P An A 1 i( )n
1 i= = + −
+
Cor.2. Formula (1) may be written as follows by using logarithm :
log A = log P + n log (1 + i)
Note. If any three of the four unknowns A, P, n and i are given, we can find the fourth unknown from the
above formula.