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Example: (TIME IS FRACTION): A sum of Rs 15,000 was borrowed for 2 ½ years at
an interest of 10% compounded annually. Find the Compound Interest and the amount
to be paid.

Solution: Given, Principal = 15,000 Rs , Rate = 10% annually

No of years = 2 ½ years
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Here, the amount for 2 years will be A = 15,000 x (1 + 10/100) =Rs 18,150.
Now, for next six months, principal amount will be 18,150 Rs. So, SI will be
SI = (15000 x ½ x 10)/100 = Rs 750
Hence, Interest for first 2 years = (18150 – 15000) =Rs 3150
And interest for next ½ year = 750 Rs.
Therefore, total CI = 3150 + 750 = 3900 Rs.
A = P + CI = 15000 + 3900 = Rs. 18,900

INTEREST COMPOUNDED HALF YEARLY:A= P(1+ ) 2n

 Rate Compounded HALF YEARLY:
When the interest is compounded half yearly rather than yearly, then we say
that the rate =(R/2)% ,half yearly, then we need to calculate the interest twice.
And in this case, time period will get double and the rate will get half.

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 Rate Compounded QUARTERLY:A= P(1+ )

Example : Find the compound interest on 10,000 Rs for 2 years at 10% per annum
when compounded half-yearly.
Solution: Here, P = 10,000 Rs; R = 10% per annum = 5% per half - yearly;
n = 2 years = 4 half years.
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Amount A = 10,000 x ( 1 + 5/100) = Rs12,155
Thus, CI = 12,155 - 10,000 = Rs2155

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