COMPOUND INTEREST
Compound Interest : Compound interest is defined as the interest which is every time added to the principal whenever it is due. Addition is done after a fixed period, usually after a year. After the interest is added to the principla, the total amount acts as principal. Thus the difference between the original principal and final amount is called compound interest.
Principal : The money landed on interest is called principal or sum. Simple Interest : The extra money paid by the borrower is called interest. Amount : Amount = Principal + Interest.
Rate percent : Interest on Rs. 100 for 1 year is called rate per cent per annum.
Formulae fo Simple Interest : If P, R and T are principal, rate and time then S.I. is given by
S.I. = P C R C T.
100
P = 100 C S.I.
R C T
R = 100 C S.I.
P C T
T = 100 C S.I.
P C R
Compound Interest : C.I. = Amount – P
If P = principal, R = rate % p.a. and T = time (years) then
(a) Amount after T years (compounded annually)
|
= P 1 + R T
100
(b) Amount after T year (compounded half yearly)
= P (
|
R 2T
1 + 2
100
In this case rate becomes half and time becomes double.
- Amount after T year (compounded quarterly)
= P(
|
R 4T
1 + 4
100
In this case rate becomes 1/4 while time becomes 4 times.
- If the rate be p%, q% and 1% during first year, second year and third year, then amount after 3 years
= P (1+ P ) (1+ q
) (1+ r )
100 100 100
- If the interest is compounded annually but the time being as a fraction
of a year say 2 1 years then amount
|
|
2
|
= p(1=
R )2 C
1 C R 1+ 2
will be
Rate of growth
= increase in population original population
POPULATION GROWTH FORMULAE
(a) If P is the population and R% is the growth rate then in n years population
|
= P 1+ R n
100
- If P% is the growth rate during first year and q% during second year then the
population after 2 years is given by
= P (1+
P ) (1+ q )
100 100
This formula can be used for more than two years.
- If R% per annum is the decrease in population then after n years
|
n
= P 1-
100
Depreciation : It is a well known fact that the value of a machine or car or any other article decreases with time due to wear and tear. The decrease in value is called depreciation value.
Thus, if V is the value at a time t and R% p.a. is the rate of depreciation, then the value of machine after n years is given by
|
n
= V C (1-
R 100
Amount after T years is given by
|
A = P 1- R T
100
Note : (a) For 2 years the difference between the compound interest and the simple interest is equal to simple interest for 1 year on 1st year’s interest.
- The amount of the previous year is the principal for the successive year.
- The difference between the amount due at the end of two consecutive years
= simple interest for one year on the lesser amount.
- When the interest is payable half yearly, divide the rate by 2 and multiply the time by 2.
- When the interest is payable quarterly or once in 1/4th year divide the rate by 4 and multiply the time by
- There is no difference between simple interest and compound interest on the principal for first C.I. is more than S.I. after one year.
