Q1.
On a sum SI is
1/16
time of sum, and number
of years are 4 times to rate of interest . find time.
Solution.
SI =
pnr/100
⇒
x/16
=
x . 4r . r/100
r
2 =
100/64
⇒ r =
10/8
%
t = 4r = 4 x
10/8
= 5 years
Solution
Q2.
On a principal SI is
9/49
times of principal
rate of SI is equal to time (in years) find rate of SI .
Solution
Let p = x , rate = time
9x/49
=
x . r . r/100
9/49
=
r2/100
⇒ r
2 =
900/49
=
r =
30/7
= 4.29 %
Solution
Q3.
A sum of money becomes triple in 20 years . find the rate of SI .
Solution.
SI =
pxr/100
⇒ 2p =
p . 20 . r/100
⇒ r = 10 %
Solution
Q4.
Rs. 3500 is distributed in two part and both part gains same interest for two years. Rate of interest are 8% and 6% respectively .
find
the ratio of value(distributed) .
Solution.
Value will be distributed in the ratio of
1/r1t1
:
1/r2t2
1/8 x 2
:
1/6 x 2
⇒
1/16
:
1/12
⇒ 3 : 4
Solution
Q5.
Which investment is better , 5% per annum compounded quarterly or 5.12% per annum .
Solution.
effective = (1 +
0.05/4
)
4 -
1 = (1.0125)
4 - 1
= 1.05095 - 1 = 0.05095
effective = 5.095 % per annum.
so, 5.12 % is better investment .
Solution
Q6.
The compound interest , compounded annually is called ___________ .
Solution.
Nominal interest rate .
Solution
Q7.
Effective rate of interest is always greater than the nominal rate of interest.(True/False)
Solution.
True
Solution
Q8.
The effective rate equivalent to nominal rate of 9% compounded monthly .
Solution.
r
e = (1 +
r/m
)
m - 1
r
e = (1 +
0.09/12
)
12
- 1
r
e = (1.0075)
12 - 1 = 1.09380 - 1
r
e = 0.09380 =
9.38 %
Solution
Q9.
The population of a town at the beginning of the year 2001 was 1,75,000 . If the rate of increase be 52 per thousand of the population
. find the populaton at the beginning of the year 2006 .
Solution.
A = p(1 +
r/100
)
n
A = 1,75,000 (1 +
5.2/100
)
5
= 1,75,000(1.052)
5 A = 1,75,000 (1.2884830) = 2,25,485
Solution
Q10.
Amount of 3rd year (in the case of compound interest) will be the principal of 4rth years. (True/False)
Solution.
True
Solution
