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CBSE Questions for Class 11 Commerce Applied Mathematics Basics Of Financial Mathematics Quiz 8 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Basics Of Financial Mathematics
Quiz 8
What is true about deferred annuity ?
Report Question
0%
It is an annuity in which the first payment is postponed for period of times.
0%
It is annuity when payments are made at the end of each payment.
0%
It is annuity when payments are made at the beginning of each payment.
0%
None of the above
Explanation
Deferred payment annuities typically offer tax-deferred growth at a fixed or variable rate of return, just like regular annuities. Often deferred payment annuities are purchased for under-age children, with the benefit payments postponed until they reach a certain age. Deferred payment annuities can be helpful in retirement planning.
Option (A) is correct
What principal will amount to
R
s
.
1352
in
2
years at
4
%
compound interest?
Report Question
0%
R
s
.
1250
0%
1200
0%
R
s
.
1000
0%
R
s
.
1300
Explanation
Given data :
A
=
R
s
.
1352
,
r
=
4
and
n
=
2
We know that,
A
=
p
[
1
+
r
100
]
n
1352
=
p
[
1
+
4
100
]
2
1352
=
p
×
26
25
×
26
25
⇒
P
=
Rs.
1250
A merchant commences with a certain capital and gains annually at the rate of
25
%. At the end of
3
years he is worth
R
s
.
10
,
000
. What was his original capital?
Report Question
0%
R
s
.
2500
0%
R
s
.5120
0%
R
s
.
5000
0%
R
s
.
6200
Explanation
Let the original sum of the amount be
x
.
Given:
A
=
R
s
.
10
,
000
t
=
3
years
r
=
25
%
So, by using the formula to calculate the compound interest,
A
=
P
(
1
+
r
100
)
t
10
,
000
=
P
(
1
+
25
100
)
3
10
,
000
=
P
(
1
+
1
4
)
3
10
,
000
=
P
(
5
4
)
3
P
=
R
s
.
5120
Hence, the initial amount was
R
s
.
5120.
At what rate per cent compound interest does a sum of money become four fold in
2
years?
Report Question
0%
25
%
0%
50
%
0%
100
%
0%
10
%
Explanation
4
x
=
x
(
1
+
r
100
)
2
∵
(
1
+
r
100
)
2
=
4
or
1
+
r
100
=
2
or
r
=
100
%
Find the compound interest of
R
s
.
800
for
3
years at
5
p
.
c
.
Report Question
0%
R
s
.
920
0%
R
s
.
850
0%
R
s
.
926.10
0%
R
s
.
126.10
A sum of money on compound interest amounts to Rs.
9
,
680
in
2
years and to Rs.
10
,
648
in
3
years. What is the rate of interest per annum?
Report Question
0%
5
%
0%
10
%
0%
15
%
0%
20
%
Explanation
Given that Rs.
9
,
680
becomes Rs.
10
,
648
in one year
therefore,
Interest
=
Rs.
10648
−
Rs.
9
,
680
=
Rs,
968
⇒
Rate
=
Interest
×
100
P
×
t
=
968
×
100
9680
×
1
=
10
%
Thus the rate of interest per annum is
10
%
.
Which of the following comes under Annuity due?
Report Question
0%
Life insurance Premium
0%
Recurring Deposit Payments
0%
Advance Payment of monthly house rent
0%
All of the above
Explanation
An annuity is a contract aimed at generating steady income during retirement, where in lump sum payment is made by an individual to obtain certain amounts immediately or at some point of future
all of above comes under annuity.
It includes Life insurance Premium, Recurring Deposit Payments, Advance Payment of monthly house rent.
What is the least number of complete years in which a sum of money at
20
%
compound interest will be more than doubled?
Report Question
0%
7
0%
6
0%
5
0%
4
Explanation
Let Principal amount
=
R
s
P
formula of compound interest,
Amount
=
P
(
1
+
r
m
)
m
t
Acc. to question,
2
P
=
P
(
1
+
20
100
)
t
⇒
2
=
(
1.2
)
t
⇒
t
=
4
Aman gave Rs.
9500
as a loan to Megh at the rate of
4
%
p.a. compounded yearly. Megh returned the amount after two years. Calculate the interest on the first year's interest.
Report Question
0%
380
0%
270
0%
15.2
0%
40
Explanation
P
=
9500
,
R
=
4
,
T
=
2
years
Interest in
1
year
=
P
×
R
×
1
100
=
9500
×
4
100
=
380
Interest on interest
=
380
×
4
×
1
100
=
15.2
What is true about deferred annuity ?
Report Question
0%
It is an annuity when the payments are made at the end of payment period.
0%
It is an annuity when the payments are made at the beginning of payment period.
0%
It is an annuity when the payments are made at the middle of payment period.
0%
None of the above
Explanation
⇒
True statement about deferred annuity is,
−
I
t
i
s
a
n
a
n
n
u
i
t
y
w
h
e
n
t
h
e
p
a
y
m
e
n
t
a
r
e
m
a
d
e
a
t
t
h
e
e
n
d
o
f
p
a
y
m
e
n
t
p
e
r
i
o
d
.
⇒
A deferred annuity is an insurance contract designed for long-term savings.
⇒
Unlike an immediate annuity, which starts annual or monthly payments almost immediately, investors can delay payments from a deferred annuity indefinitely. During that time, any earnings in the account are tax-deferred.
A sum of money put out at compound interest amount in two years to
R
s
.
2809
, and in three years to
R
s
.
2977.54
. Find the rate per cent
Report Question
0%
6
%
0%
10
%
0%
4
%
0%
3
%
Explanation
Difference in amounts
=
2977.54
−
2809
=
R
s
.
168.54
R
s
.168
.54
is the interest on
R
s
.
2809
in one year
R
a
t
e
=
Difference in amounts
Initial amount
×
100
R
a
t
e
=
168.54
2809
×
100
R
a
t
e
=
6
%
(The rate is per annum)
The first year's interest on a sum of money lent at
8
% compound interest is
R
s
.
48
. The second year's amount is
Report Question
0%
R
s
.
48
0%
R
s
.
51.48
0%
R
s
.
56.48
0%
R
s
.
96
A sum of money placed at compound interest doubles itself in
4
years. In how many years will it amount to eight times itself?
Report Question
0%
16
0%
8
0%
12
0%
20
The compound interest on a certain sum for
2
years is
R
s
.
40.80
and the simple interest is
R
s
.
40
. Find the rate p.c.?
Report Question
0%
R
s
.
4
0%
4
%
0%
R
s
.
0.80
0%
8
%
The calculation of interest on the interest of principal amount is called
Report Question
0%
simple interest
0%
compound interest
0%
multiple interest
0%
interest quarterly compounded
Explanation
The calculation of interest on the interest of principal amount is called
C
o
m
p
o
u
n
d
i
n
t
e
r
e
s
t
.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Compound interest is standard in finance and economics.
Anagha borrowed Rs.
70
,
000
from her friend at the rate of
3.5
%
p.a.compounded yearly. She returned the amount after three years. So calculate interest of first year and second year .
Report Question
0%
R
s
.2
,
450
,
85.75
0%
R
s
.2
,
450
,
2
,
450
0%
R
s
.2
,
450
,
2
,
535.75
0%
R
s
.2
,
450
,
2100
Explanation
P
=
70000
,
R
=
3.5
%
Interest in
1
st year
=
P
×
R
×
T
100
=
70000
×
3.5
×
1
100
=
2450
Now,
(
2450
+
P
)
will be principal amount for
2
nd year since interest is compounded yearly
Interest in
2
nd year
=
P
′
×
R
×
T
100
=
(
2450
+
70000
)
×
3.5
×
1
100
=
724.5
×
3.5
=
2535.75
Megha lended Rs.
8000
as a loan for
4
years at the rate
4
%
compounded annualy. Calculate the interest she will recive by the method of simple interest.
Report Question
0%
8963.26
0%
9358.86
0%
1358.86
0%
9863.25
Explanation
P
=
8000
,
R
=
4
%,
T
=
4
Interest in
1
st year
=
P
×
R
×
T
100
=
8000
×
4
×
1
100
=
320
Now, Principal amount will be
(
P
+
320
)
since the interest in compounded annually.
Interest in
2
nd year
=
P
′
×
R
×
T
100
=
8320
×
4
×
1
100
=
332.8
Now,
P
″
Interest in
3
rd year
=\cfrac { 8652.8\times 4\times 1 }{ 100 } =346.112
Interest in
4
th year
=\cfrac { (346.112+8652.8)\times 4\times 1 }{ 100 } =359.956
Total interest
=320+332.8+346.112+359.95
=1358.86
The bank offers senior citizens intrest at the rate
9\%
p.a compounded yearly on a fixed deposit. What interest will be received at the end of
5
years if Rs.
10,000
are deposited. Calculate by the method of simple interest.
Report Question
0%
5386.23
0%
5500.23
0%
6523.65
0%
4367.78
Explanation
P=10000,R=9,T=5
yrs
Interest in
1
st year
=\cfrac { P\times R\times T }{ 100 }
=\cfrac { 10000\times 9\times 1 }{ 100 }
=900
P'=(900+10000)
Interest in
2
nd year
=\cfrac { 10900\times 9\times 1 }{ 100 } =981
Interest in
3
rd year
=\cfrac { 11881\times 9\times 1 }{ 100 }
=1069.29
Interest in
4
th year
=\cfrac { 12950.29\times 9\times 1 }{ 100 }
=1165.5261
Interest in
5
th year
=\cfrac { 14115.81\times 9\times 1 }{ 100 }
=1270.42
Total interest
=900+981+1069.29+1165.52+1270.42
=5386.23
A businessman borrowed the Rs.
45
lakh for two years at the rate
2.5\%
p.a. compounded annually. Calculate the compound interest by simple interest method.
Report Question
0%
2,23000
0%
2,27,812.5
0%
5,65,563
0%
2,00,000
Explanation
\Rightarrow
Here, Principal amount for first year is
Rs.45,00,000
and
R=2.5\%
.
\Rightarrow
Interest for first year =
\dfrac{4500000\times 2.5}{100}=Rs.1,12,500
\Rightarrow
Principal amount for second year =
Rs.4500000+Rs.112500=Rs.46,12,500
\Rightarrow
Second year interest =
\dfrac{4612500\times 2.5}{100}=Rs.1,15,312.5
\Rightarrow
Total interest for 2 yeras =
Rs.1,12,500+Rs.1,15,312.5=Rs.2,27,812.5
Amar gave Rs.
50,000
as a loan to Amir at the rate of
4\%
p.a. Amir return the amount after two years. Calculate the interest on the first year's interest.
Report Question
0%
200
0%
70
0%
80
0%
60
Explanation
1
year interest
=\cfrac { P\times R\times T }{ 100 }
=\cfrac { 50000\times 4\times 1 }{ 100 } =2000
Interest of
1
year interest
=\cfrac { \left( { P }^{ ' }\times R\times T \right) }{ 100 }
=\cfrac { 2000\times 4\times 1 }{ 100 }
=80
An industrialist borrowed the
Rs\ 75,000
for two years at the rate
2.5\%
p.a.compounded annually. Calculate the total amount compound interest by simple interest method.
Report Question
0%
2750
0%
3750
0%
78,795
0%
78,796.87
Explanation
P=75000,R=2.5
%, Time
=2
yrs
Interest in
1
st year
=\cfrac { P\times R\times T }{ 100 }
=\cfrac { 75000\times 2.5\times 1 }{ 100 }
=1875
P'=(1875+P)
Interest in
2
nd year
=\cfrac { { P }^{ ' }\times R\times T }{ 100 }
=\cfrac { 76875\times 2.5\times 1 }{ 100 }
=1921.875
Total interest
=1875+1921.875
=3796.875
Total amount=Principal
+
Total interest
=75000+3796.875
=78796.875
Depreciation is the process of valuation of asset.
Report Question
0%
True
0%
False
Explanation
Depreciation means fall in the value of assets. The net result of an asset's depreciation is that sooner or later the asset will become useless. Depreciation is the process of reduction in the value of asset.
What principal will amount to Rs.
9,744
in two years, if the rates of interest for successive years are
16
% and
20
% respectively?
Report Question
0%
7000
0%
8000
0%
5000
0%
9000
Explanation
\Rightarrow
Let the principal (P) be
Rs.x
.
\Rightarrow
Rate of interests for two successive years are
(R_1)\,\,16\%
and
(R_2)\,\,20\%
.
\Rightarrow
A=P(1+\dfrac{R_1}{100})(1+\dfrac{R_2}{100})
\Rightarrow
9744=x(1+\dfrac{16}{100})(1+\dfrac{20}{100})
\Rightarrow
9744=x\times \dfrac{29}{25}\times {6}{5}
\Rightarrow
9744=\dfrac{174}{125}x
\therefore
x=\dfrac{9744\times 125}{174}
=56\times 125=Rs.7000
\therefore
Hence, principal =
Rs.7000
.
A sum of Rs.
8,000
is invested for
1
years at
10
% per annum compound interest. Calculate :interest for the second year.
Report Question
0%
880
0%
860
0%
800
0%
1000
Explanation
\Rightarrow
Here we have,
P=Rs.8000,\, T=1
and
R=10\%
\Rightarrow
I=\dfrac{P\times R\times T}{100}
\Rightarrow
I=\dfrac{8000\times 10\times 1}{100}
\Rightarrow
I=Rs.800
\therefore
Interest for first year is
Rs.800
.
\Rightarrow
Interest for second year =
800+\dfrac{10}{100}\times 800=800+80=Rs.880
Calculate compound interest for Rs
15,000
for
1
year at
16
% compounded semi -annually.
Report Question
0%
Rs.
3172
0%
Rs.
2496
0%
Rs.
3000
0%
Rs.
2572
Explanation
Given:
\Rightarrow
P=
Rs.
15000,\,T=1\ year=2
and
R=16\%
R_{eq}=8\%
Since, semi-annually compounded.
T_{eq}=2.T= 2.
Since, semi-annually compounded.
\Rightarrow
A=P(1+\dfrac{R_{eq}}{100})^{T_{eq}}
\Rightarrow
A=15000\times (1+\dfrac{8}{100})^2
\Rightarrow
A=15000\times (\dfrac{27}{25})^2
\Rightarrow
A=15000\times (\dfrac{729}{625})
\therefore
A=
Rs.
17496
\therefore
C.I.=A-P=
Rs.
17496-
Rs.
15000=
Rs.
2496.
Ranjana borrowed the money Rs
1,00,000
for
3
years at the rate
3.5\%
p.a. compounded annually. Calculate interest to be paid.
Report Question
0%
10871.78
0%
1000.8
0%
8710.68
0%
245
Explanation
\Rightarrow
Here, Principal amount for first year =
Rs.1,00,000
\Rightarrow
First year Interest =
\dfrac{100000\times 3.5}{100}=Rs.3500
\Rightarrow
Principal amount for second year =
Rs.1,00,000+Rs.3500=Rs.1,03,500.
\Rightarrow
Second year interest =
\dfrac{103500\times 3.5}{100}=Rs.3622.5
\Rightarrow
Principal amount for third year =
Rs.1,03,500+Rs.3622.5=Rs.1,07,122.5
\Rightarrow
Third year interest =
\dfrac{107122.5\times 3.5}{100}=Rs.3749.28
\therefore
Total Interest =
Rs.3500+Rs.3622.5+Rs.3749.28=Rs.10871.78
A man lends Rs.
12,500
at
12
% for the first year, at
15
% for the second year and at
18
% for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. for the first year and the compound interest for the third year.
Report Question
0%
\text{Rs }1,498
0%
\text{Rs }1,598
0%
\text{Rs }1,298
0%
\text{Rs }1,398
A bank pays interest at the rate of
8\%
per annum compounded yearly. Find the interest by simple interest method if
Rs.\ 8000
was deposited for
3
years.
Report Question
0%
Rs.\ 1000
0%
Rs.\ 2077.7
0%
Rs.\ 2000
0%
Rs.\ 3456
Explanation
P=Rs.\ 8000,R=8
%, Time period
=3
years
Interest in
1
st year
=\cfrac { P\times R\times T }{ 100 }
=\cfrac { 8000\times 8\times 1 }{ 100 }
=Rs.\ 640
Principal amount for
2
nd year will be,
P'=P+640
=Rs.\ 8000+Rs.\ 640
=Rs.\ 8640
Interest in
2
nd year
=\cfrac { 8640\times 8 }{ 100 }
=Rs.\ 691.2
Principal amount for
2
nd year will be,
P''=P'+691.2
=Rs.\ 8640+Rs.\ 691.2
=Rs.\ 9331.2
Interest in
3
rd year
=\cfrac { 9331.2\times 8 }{ 100 }
=Rs.\ 746.5
So, total interest
=640+691.2+746.5
=Rs.\ 2077.69
\approx Rs.\ 2077.7
The population of a town
3
years ago was Rs.
50,000
.If the population in these three years has increased at the rate of
10\%,15\%
and
8\%
respectively, find the present population.
Report Question
0%
Rs.
68,210
0%
Rs.
68,310
0%
Rs.
68,410
0%
Rs.
68,510
Explanation
Let
P=.50,000
and
R_1=10\%,\\ R_2=15\%,\\ R_3=8\%
.
Present population =
P\times \left (1+\dfrac{R_1}{100}\right)\left (1+\dfrac{R_2}{100}\right)\left (1+\dfrac{R_3}{100}\right)
On substituiting the given values,
Present population
=
50000\times \left (1+\dfrac{10}{100}\right)\times \left (1+\dfrac{15}{100}\right)\times \left (1+\dfrac{8}{100}\right)
=
50000\times \dfrac{11}{10}\times \dfrac {23}{20}\times \dfrac{27}{25} =68310
Therefore, p
resent population
=
68310
.
If
600
dollars is deposited in a bank account for
4
years at
8
% per annum . Calculate interest using compound interest formula.
Report Question
0%
216
0%
216.3
0%
220.6
0%
224.8
Explanation
Amount at the end of
4
years
=600(1+0.08)^4
=816.29
Compound interest
=816.29-600=216.29
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