IMPORTANT FACTS AND FORMULAE
1.. Principal: The money borrowed or lent out for a certain period
is called the
principal or
the sum.
2. Interest: Extra money paid for using
other's money is called interest.
3. Simple Interest (S.I.) : If the interest on
a sum borrowed for a certain period is reckoned uniformly, then it is called simple
interest.
Let Principal = P, Rate = R% per annum (p.a.) and
Time = T years. Then,
(i)
S.I. = (P*R*T
)/100
(ii) P=(100*S.I)/(R*T)
;R=(100*S.I)/(P*T) and T=(100*S.I)/(P*R)
SOLVED EXAMPLES
Ex. 1. Find the simple interest on Rs.
68,000 at 16 2/3% per annum for 9 months.
Sol. P =
Rs.68000,R = 50/3% p.a and T = 9/12 years
= 3/4years.
\ S.I. = (P*R*T)/100 = Rs.(68,000*(50/3)*(3/4)*(1/100))= Rs.8500
Ex. 2. Find the simple
interest on Rs. 3000 at 6 1/4% per annum for the period from
4th Feb., 2005 to 18th April, 2005.
Sol. Time = (24+31+18)days = 73 days = 73/365 years =
1/5 years.
P = Rs.3000
and R = 6 ¼ %p.a = 25/4%p.a
\S.I. = Rs.(3,000*(25/4)*(1/5)*(1/100))= Rs.37.50.
Remark : The day on which money is deposited is not counted
while the day on which money is withdrawn is counted .
Ex. 3. A sum at simple interests at 13 ½ % per annum
amounts to Rs.2502.50 after 4 years find the sum.
Sol. Let sum
be Rs. x then , S.I.=Rs.(x*(27/2)
*4*(1/100) ) =
Rs.27x/50
\amount
= (Rs.
x+(27x/50)) =
Rs.77x/50
\
77x/50 = 2502.50 Û
x = 2502.50 * 50 = 1625
77
Hence , sum =
Rs.1625.
Ex. 4. A sum of Rs. 800
amounts to Rs. 920 in 8 years at simple intere
interest
rate is increased by 8%, it would amount to bow mucb ?
Sol.
S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _
. R = ((100 x 120)/(800*3) ) % = 5%.
New rate = (5
+ 3)% = 8%.
New S.l. = Rs. (800*8*3)/100
= Rs. 192.
: New amount = Rs.(800+192) =
Rs. 992.
Ex.
5. Adam borrowed some money at the rate of 6% p.a. for the first two years ,
at the rate of 9% p.a. for the next
three years , and at the rate of 14% p.a. for the period beyond five years. 1£
he pays a total interest of Rs. 11, 400 at the end of nine years how much money
did he borrow ?
Sol. Let the sum borrowed be x. Then,
(x*2*6)/100 + (x*9*3)/100 + (x*14*4)/100 = 11400
Û
(3x/25 + 27x/100 + 14x / 25) = 11400 Û 95x/100 = 11400 Û x =
(11400*100)/95 = 12000.
Hence , sum borrowed = Rs.12,000.
Ex. 6. A
certain sum of money amounts to Rs. 1008 in 2 years and to Rs.1164 in 3 ½
years. Find the sum and rate of interests.
Sol..
S.I. for 1 ½ years = Rs.(1164-1008) = Rs.156.
S.l.
for 2 years = Rs.(156*(2/3)*2)=Rs.208
Principal = Rs. (1008 - 208) = Rs.
800.
Now, P = 800, T = 2 and S.l. = 208.
Rate =(100*
208)/(800*2)% = 13%
Ex. 7. At
what rate percent per annum will a sum of money double in 16 years.
Sol.. Let principal = P. Then,
S.l. = P and T = 16 yrs.
\Rate = (100 x P)/(P*16)% =
6 ¼ % p.a.
Ex. 8. The simple interest on a sum of money is 4/9 of
the principal .Find the rate percent and time, if both are numerically equal.
Sol. Let sum = Rs. x. Then, S.l. =
Rs. 4x/9
Let rate = R% and time = R years.
Then, (x*R*R)/100=4x/9 or R2
=400/9 or R = 20/3 = 6 2/3.
\Rate = 6 2/3 % and Time = 6 2/3 years = 6 years 8
months.
Ex.
9. The simple interest on a certain sum of money for 2 l/2 years at 12% per
annum is Rs. 40 less tban the
simple interest on the same sum for 3 ½
years at 10% per annum. Find the sum.
Sol. Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40
Û
(7x/20)-(3x/10)=40
Ûx = (40 * 20) = 800.
Hence, the sum is Rs. 800.
Ex.
10. A sum was put at simple interest at a certain rate for 3 years. Had it been
put at 2% higher rate, it would have fetched Rs.
360 more. Find the sum.
Sol. Let sum = P and original rate =
R.
Then, [ (P*(R+2)*3)/100] – [ (P*R*3)/100] = 360.
Û 3PR
+ 6P - 3PR = 36000 Û
6P=36000 Û
P=6000
Hence, sum = Rs. 6000.
Ex.
11. What annual instalment will discharge a debt of Rs. 1092 due in 3 years
at 12% simple interest?
.
Sol . Let each Instalment be Rs. x
Then,
( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1092
Û ((28x/25)
+ (31x/25) + x) = 1092 Û
(28x+31x+25x)=(1092*25)
Û x=
(1092*25)/84 = Rs.325.
\ Each instalment = Rs. 325.
Ex. 12. A sum of Rs. 1550 is lent out into two
parts, one at 8% and another one at
6%. If the total annual income is Rs. 106, find
the money lent at each rate.
Sol. Let the sum lent at 8% be Rs. x and
that at 6% be Rs. (1550 - x).
\((x*8*1)/100) + ((1550-x)*6*1)/100=106
Û8x + 9300 –6x=10600 Û 2x =
1300 Û x = 650.
\
Money lent at 8% = Rs. 650. Money lent at 6% = Rs. (1550 - 650) = Rs. 900.
