What will be the time period for a sum taken for 2 years at 8% per annum compounded half yearly?

1. Percent:

(i) Per cent means per hundred or for every hundred.

(ii) A fraction with its denominator as 100 is called a per cent and is equal to that per cent as is the numerator.

(iii) A ratio with its second term 100 is also called a per cent.

2. Converting to Per cent:

(i) To convert a fraction into a per cent, we multiply the fraction by 100.

(ii) To convert a ratio into a per cent, we write it as a fraction and multiply it by 100.

(iii) To convert a decimal into a per cent, we shift the decimal point two places to the right.

3. Converting from Per cent:

(i) To convert a per cent into a fraction, we drop per cent sign % and divide the remainder by 100.

(ii) To convert a per cent into a ratio, we drop per cent sign % and form a ratio with the remaining number as the first term and 100 as the second term.

(iii) To convert a per cent into a decimal, we drop per cent sign % and shift the decimal point two places to the left.

4. Increase Per cent of a Value:

Increase %= Increase original value×100%

5. Decrease Per cent of a Value:

Decrease %= Decrease original value×100%

6. Profit:

(i) Profit=S.P.-C.P.

(ii) Profit %=Profit C.P. ×100 or Profit= C.P. × Profit %100

(iii) S.P.=C.P.100+ Profit%100

(iv) C.P.=100×S.P.(100+ Profit%)

7. Loss:

(i) Loss=C.P.-S.P.

(ii) Loss %=LossC.P.×100 or Loss=C.P. ×Loss %100

(iii) S.P.=C.P.100-Loss %100

(iv) C.P.=100×S.P.100-Loss %

8. Discount:

(i) Discount=M.P.-S.P.

(ii) Rate of Discount=Discount %= Discount M.P.×100

(iii) S.P.=M.P.100-Discount %100

(iv) M.P.=100×S.P.(100-Discount %)

9. Value added tax (VAT) is charged on the selling price of an article.

10. If the borrower and the lender agree to fix up a certain interval of time (say, a year or a half-year or a quarter of a year etc.) so that the amount at the end of an interval becomes the principal for the next interval, then the total interest over all the intervals calculated in this way is called the compound interest and is denoted by C.I. Also, C.I.=Amount−Principal.

11. Compound Interest:

(i) Let P be the principal and the rate of interest be R% per annum. If the interest is compounded annually, then the amount A and the compound interest C.I. at the end of n years are given by

A=P1+R100n and, C.I.=A-P=P1+R100n-1 respectively.

(ii) Let P be the principal and the rate of interest be R1% for first year, R1% for second year, R1% for third year and so on and in last Rn% for the nth year. Then, the amount A and the compound interest C.I. at the end of n years are given by

A=P1+R11001+R2100…1+Rn100 and, C.I.=A-P respectively.

(iii) Let P be the principal and the rate of interest be R% per annum. If the interest is compounded annually but time is the fraction of a year, say 514 years, then amount A is given by

A=P1+R110051+R4100 and, C.I.=A-P

12. Population Growth:

(i) Let P be the population of a city or town at the beginning of a certain year and the population grows at a constant rate of R% per annum, then

Population after n years=P1+R100n

(ii) Let P be the population of a city or a town at the beginning of a certain year. If the population grows at the rate of R1% during first year and R2% during second year, then

Population after 2 years=P1+R1100×1+R2100.

Calculate the amount and compound interest on:

(a) Rs 10,800 for 3 years at 121/2 % per annum compounded annually.

(b) Rs 18,000 for 21/2 years at 10% per annum compounded annually.

(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly.

(You could use the year by year calculation using SI formula to verify.)

(e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.