Basics of Financial Mathematics Test 12

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Basics of Financial Mathematics Test 12

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Question 1
1 / -0

The population of a town increases by 5% annually. If the population in 2009 is 1,38,915, what was it in 2006 ?

A
100,000

B
110,000

C
120,000

D
130,000

Solution

Let the population in 2006 be $x$ .
Pop. in $\displaystyle 2009=x\times \left ( 1+\cfrac{5}{100} \right )^{3}$
$\Rightarrow 1,38,915=x\times \left ( \cfrac{21}{20} \right )^{3}$
$\Rightarrow x=\cfrac{138915\times 8000}{9261}=120000$
Question 2
1 / -0

The C.I. on a sum of money for 2 years is Rs. 832 and the S.I. on the same sum for the same period is Rs. 800. The difference between the C.I and S.I. for 3 years will be

A
Rs. 48

B
Rs. 66.56

C
Rs. 98.56

D
None of these

Solution

Given that simple interest for 2 years is Rs.800
i.e., Simple interest for 1st year is Rs.400 and simple interest for 2nd year is also Rs.400
Compound interest for 1st year will be 400 and compound interest for 2nd year will be $832 - 400 = 432$
We can see that compound interest for 2nd year is more than simple interest for 2nd year by $432 - 400 = Rs.32$
Rs. 32 is the interest obtained for Rs.400 for 1 year
$R = \frac{100\times SI}{PT} = \frac{100 \times 32}{400\times1} = 8$ %
Difference between compound and simple interest for the 3rd year
= Simple Interest obtained for Rs.832 $=\frac{PRT}{100} = \frac{832\times 8\times 1}{100} = 66.56$
Total difference between the compound and simple interest for 3 years $= 32 + 66.56 = Rs.98.56$
Question 3
1 / -0

A bank offers $5\%\ C.I.$ calculated on a half-yearly basis. A customer deposits $Rs.\ 1600$ each on 1st January and $1st$ July of a year. At the end of the year, the amount he would have gained by way of interest is

A
$Rs.\ 120$

B
$Rs.\ 121$

C
$Rs.\ 122$

D
$Rs.\ 123$

Solution

Amount=1600
Rate of interest=5%
Time =Half yearly basic
$amount=1600\times (1+\frac{5}{2\times 100})^2+ 1600\times (1+\frac{5}{2\times 100})$
$= 1600\times \frac{205}{200}+\frac{205}{200}+1600\times \frac{205}{200}$
$=1681+1640=3321 Rs.$
$C.I.=3321-3200=121 Rs.$
Question 4
1 / -0

A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?

A
Rs. 565.25

B
Rs. 635

C
Rs. 662.02

D
Rs. 666.50

Solution

For 1 st year
$Principal=200$
$Amount=200\times (1+\frac{5}{100})$
$=200\times \frac{105}{100}$
$=210 Rs.$
For second year
$Principal=200+210=410 Rs.$
$Amount=410\times (1+\frac{5}{100})$
$=410\times \frac{105}{100}$
$=430.5 Rs.$
For 3 rd year
$Principal=430.5+200=630.5 Rs$
$Amount =630.5\times(1+\frac{5}{100})$
$=630.5\times \frac{105}{100}$
$=662.02 Rs.$
Question 5
1 / -0

A tree grows annually by one-eighth of its height. By how much will it grow after 2 years, if it stands today 64 cm high?

A
72 cm

B
74 cm

C
75 cm

D
81 cm

Solution

Present height of tree=64cm
It grow annually by one-eighth of its height
Then it grow in first year= $\frac{1}{8}\times 64=8 cm$
Then total height= $64+8=72$
In second year it grow = $\frac{1}{8}\times 72=9 cm$
then total height after 2 year= $72+9=81 cm$
Question 6
1 / -0

The population of a village is 10000. If the population increases by 10% in the first year, by 20% in the second year, and due to mass exodus, it decreases by 5% in the third year, what will be its population after 3 years ?

A
10,540

B
11,540

C
12,540

D
13,540

Solution

Population after 3 years $\displaystyle =10000\left ( 1+\frac{10}{100} \right )\left ( 1+\frac{20}{100} \right )\left ( 1-\frac{5}{100} \right )$
$\displaystyle =10000\times \frac{11}{10}\times \frac{6}{5}\times \frac{19}{20}=12540$
Question 7
1 / -0

What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?

A
Rs. 31

B
Rs. 32.10

C
Rs. 40.40

D
Rs. 64.10

Solution

Principal=1000 Rs.
Time=4 years
Rate of interes=10%
Then Simple interest $=\frac{1000\times 10\times 4}{100}=400 Rs.$
Compound interest $=$ Amount $-$ Principal
Amount $=1000(1+\frac{10}{100})^4$
$\Rightarrow 1000\times \frac{110}{100}\times \frac{110}{100}\times \frac{110}{100}\times \frac{110}{100}\times$
$\Rightarrow 1464.10 Rs.$
$C.I.=1464.10-4000=464.10 Rs.$
Difference between C.I and S.I.= $464.10-400=64.10 Rs.$
Question 8
1 / -0

On what sum of money lent out at 9% per annum for 6 years does the simple interest amounts to Rs. 810?

A
Rs. 1000

B
Rs. 1500

C
Rs. 1200

D
None

Solution

Simple Interest $=\text{Rs.}\ 810$
$R= 9\%$
$T = 6\ \text{years}$
$P=?$

According to the formula of Simple Interest:
Simple Intrest $I\, =\, \displaystyle \frac {P\times T\times R}{100}$

$P\, =\, \displaystyle \frac {100 \times I}{T\times R}$

$=\, \displaystyle \frac {100 \times 810}{6 \times 9}$
$=\, \text{Rs.}\, 1500$
Question 9
1 / -0

A sum of Rs. 12,000 deposited at compound interest doubles after 5 years. After 20 years it will become

A
Rs. 1,20,000

B
Rs. 1,92,000

C
Rs. 1,24,000

D
Rs. 96,000

Solution

According to the question
After 5 year
$12000\times (1+\frac{R}{100})^5=24000$
$(1+\frac{R}{100})^5=2$
After 10 year
$(((1+\frac{R}{100})^5)^4)=2^4$
$(1+\frac{R}{100})^{20}=16$
$P(1+\frac{R}{100})^{20}=16\times P=16\times 12000=192000$
Question 10
1 / -0

A sum of Rs. 100 at CI becomes Rs. 300 in 4 years. What will it amount to in 12 years?

A
Rs. 2,700

B
Rs. 2,400

C
Rs. 2,200

D
Rs. 3,700

Solution

Principal(P)=100
After 4 years amount= $3\times P=3\times 100=300 Rs.$
After 8 years amount = $3\times P=3\times 300=900 Rs$
After 12 years amount= $3\times P=3\times 900=2700 Rs.$

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Basics of Financial Mathematics Test 12

Result

Basics of Financial Mathematics Test 12

Score

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SHARING IS CARING

Question 1

100,000

110,000

120,000

130,000

Solution

Question 2

Rs. 48

Rs. 66.56

Rs. 98.56

None of these

Solution

Question 3

Rs. 120Rs.\ 120Rs. 120

Rs. 121Rs.\ 121Rs. 121

Rs. 122Rs.\ 122Rs. 122

Rs. 123Rs.\ 123Rs. 123

Solution

Question 4

Rs. 565.25

Rs. 635

Rs. 662.02

Rs. 666.50

Solution

Question 5

72 cm

74 cm

75 cm

81 cm

Solution

Question 6

10,540

11,540

12,540

13,540

Solution

Question 7

Rs. 31

Rs. 32.10

Rs. 40.40

Rs. 64.10

Solution

Question 8

Rs. 1000

Rs. 1500

Rs. 1200

None

Solution

Question 9

Rs. 1,20,000

Rs. 1,92,000

Rs. 1,24,000

Rs. 96,000

Solution

Question 10

Rs. 2,700

Rs. 2,400

Rs. 2,200

Rs. 3,700

Solution

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$Rs.\ 120$

$Rs.\ 121$

$Rs.\ 122$

$Rs.\ 123$