7 INTEREST
Read this please:
Raju borrowed Rs. 1000 from Ramesh. After some days Raju paid back Rs. 1200 to Ramesh. Means
Raju paid Rs.200 excess than the amount he borrowed from Ramesh.
This excess amount is called interest.
The total amount of money borrowed by Raju from Ramesh is called the Princ ipal or Sum.
The money paid back to Ramesh, which is the combination ofboth Principal and interest is called the
Amount.
So, Amount = Principal + Interest
Rate of interest:
The interest is usually charged according to a specified term, which is expressed as some per cent of
the principal and is called the rate of interest for the fixed period oftime.
Ifthe fixed period is a year, the rate ofinterest is charged annually.
Ifthe fixed period is six months, the rate of interest is charged semi-annually
Ifthe fixed period is three months, the rate ofinterest is charged quarterly.
Ifthe fixed period is a month, the rate ofinterest is charged monthly.
Example:
Iftherate ofinterest is 10% per annum, thenthe interest payable on Rs. 100 tor one year is Rs. 10.
Simple Interest:
When the interest is payable on the principal only, it is called the simple interest. It is the interest
calculated on the principal for the entire period it is borrowed. It is denoted by S.
Example:
S.I. on Rs. 100 at 10% per annum will be Rs. 10each year.
Al the end of one year, the total amount will be Rs. 100+ 10- R>. I10.
Atheend of second year, the total amount will be Rs.100+10-10 Rs.I20 and so on.
, Formulae:
lI P stands for Principal, R the rate per cent per annum, T the number oryears, Athe amount and s
1. S.
the simple interest then
S.I.=PXTxR
100
P 100xS.I.
2 RxT
3. R 100x
PxT
S./%
4. T 100xS.I .
years
PxR
5. Amount,A P1+ 100
=
100x A
6 Ifa certain sum in T years at R% per annum amounts to Rs.A, then the sum wil
de 100 (Rx T:
100x A
1. The annual payment that will discharge a debt
ofRs.A due in T years at R% per annum=10OT
2
8. Ifa certain sum is invested inntypes ofinvestments in such a
that equal amount is obtained on
manner
each investment where interest rates are
R,,R,. ..R respectively and time periods and time
are
T,l2 T,respectively, then the ratio in which the amounts are invested is periods
1 1
100 RT 100 +R2T2 100+Rn'n
9. Ifa certain sum ofmoney becomes n times itser ini
years a s.l., then the rate
of interest per annum
is, R 100(n-)%%. T
10 Ifacertain sum of money becomes n times iiselat k o
per annum S.I. in T
years vears
thanT100(n-1
R
11. Ifa certain sum of money becomes n times tsell inTyears at a
m-1
simple interest, then the
it will become mtimes it self is given byT n-1 time T in which
years.
12. Ifthe rate of interest
(R) changes from R, to R, and P, T are conc.
PT then
Change in S.l. =00
100 (R R2).
Read this please:
Raju borrowed Rs. 1000 from Ramesh. After some days Raju paid back Rs. 1200 to Ramesh. Means
Raju paid Rs.200 excess than the amount he borrowed from Ramesh.
This excess amount is called interest.
The total amount of money borrowed by Raju from Ramesh is called the Princ ipal or Sum.
The money paid back to Ramesh, which is the combination ofboth Principal and interest is called the
Amount.
So, Amount = Principal + Interest
Rate of interest:
The interest is usually charged according to a specified term, which is expressed as some per cent of
the principal and is called the rate of interest for the fixed period oftime.
Ifthe fixed period is a year, the rate ofinterest is charged annually.
Ifthe fixed period is six months, the rate of interest is charged semi-annually
Ifthe fixed period is three months, the rate ofinterest is charged quarterly.
Ifthe fixed period is a month, the rate ofinterest is charged monthly.
Example:
Iftherate ofinterest is 10% per annum, thenthe interest payable on Rs. 100 tor one year is Rs. 10.
Simple Interest:
When the interest is payable on the principal only, it is called the simple interest. It is the interest
calculated on the principal for the entire period it is borrowed. It is denoted by S.
Example:
S.I. on Rs. 100 at 10% per annum will be Rs. 10each year.
Al the end of one year, the total amount will be Rs. 100+ 10- R>. I10.
Atheend of second year, the total amount will be Rs.100+10-10 Rs.I20 and so on.
, Formulae:
lI P stands for Principal, R the rate per cent per annum, T the number oryears, Athe amount and s
1. S.
the simple interest then
S.I.=PXTxR
100
P 100xS.I.
2 RxT
3. R 100x
PxT
S./%
4. T 100xS.I .
years
PxR
5. Amount,A P1+ 100
=
100x A
6 Ifa certain sum in T years at R% per annum amounts to Rs.A, then the sum wil
de 100 (Rx T:
100x A
1. The annual payment that will discharge a debt
ofRs.A due in T years at R% per annum=10OT
2
8. Ifa certain sum is invested inntypes ofinvestments in such a
that equal amount is obtained on
manner
each investment where interest rates are
R,,R,. ..R respectively and time periods and time
are
T,l2 T,respectively, then the ratio in which the amounts are invested is periods
1 1
100 RT 100 +R2T2 100+Rn'n
9. Ifa certain sum ofmoney becomes n times itser ini
years a s.l., then the rate
of interest per annum
is, R 100(n-)%%. T
10 Ifacertain sum of money becomes n times iiselat k o
per annum S.I. in T
years vears
thanT100(n-1
R
11. Ifa certain sum of money becomes n times tsell inTyears at a
m-1
simple interest, then the
it will become mtimes it self is given byT n-1 time T in which
years.
12. Ifthe rate of interest
(R) changes from R, to R, and P, T are conc.
PT then
Change in S.l. =00
100 (R R2).
