Basics of Financial Mathematics Test 9

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Basics of Financial Mathematics Test 9

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Question 1
1 / -0

Calculate the compound interest for the third year on $Rs.\ 7,500$ invested for $5$ years at $10\%$ per annum.

A
$Rs. 907.50$

B
$Rs.\ 2482.50$

C
$Rs.\ 2582.50$

D
$Rs.\ 982.50$

Solution

$A=P\left(1+\dfrac{R}{100}\right)^T$
$P=Rs.\ 7500, R=10% , T=3$ years

$A=7500\left(1+\dfrac{10}{100}\right)^3$

$A=7500\times \dfrac{110}{100}\times \dfrac{110}{100}\times \dfrac{110}{100}$

$A=\dfrac{75\times 121\times 11}{10}$

$A=Rs. 9982.50$

For $2$ years
$A=7500\left(1+\dfrac{10}{100}\right)^2$

$A=7500\times \dfrac{110}{100}\times \dfrac{110}{100}$

$A=75\times 121$

$A=Rs. 9075$

Compound interest for third year = $Rs.\ 9982.50-9075=907.50 Rs.$

Hence, option A.
Question 2
1 / -0

The value of a machine depreciated by $10 \%$ per year during the first two years and $15 \%$ per year during the third year. Express the total depreciation of the machine, as per cent, during the three years.

A
$43.21 \%$

B
$31.15 \%$

C
$23.14 \%$

D
$18.34 \%$

Solution

Lets Price of article is $100$
Dep value after $1$ year $=100-\dfrac{100\times10}{100}$ = $90$

Dep. value after $2$ year $=90- \cfrac{90\times 10}{100}= 81$
Dep. value after $3$ years $=81-\cfrac{81\times 15}{100}= 68.85$
Total Dep. $=100-68.85$ = $31.15 \%$
Question 3
1 / -0

Calculate the amount and the compound interest on Rs. $6,000$ in $3$ years at $5\%$ per year.

A
Rs. 6,945.75 and Rs. 945.75

B
Rs. 6,845.75 and Rs. 945.75

C
Rs. 6,945.75 and Rs. 945.85

D
Rs. 6,945.75 and Rs. 945.70

Solution

C.A = $P\left (1+ \frac{R}{100} \right )^{T}$

Given $R=5\%$ and $P=6000 ,T=3$

So C.A = $6000\left (1+ \frac{5}{100} \right )^{3}$

So C.A = $6000\left ( \frac{105}{100} \right )\left ( \frac{105}{100} \right )\left ( \frac{105}{100} \right )$

C.A $=6945.75$ Rs

C.I $=6945.75 -6000=945.75$ Rs
Question 4
1 / -0

Calculate the amount and the compound interest on Rs. $16,000$ in $3$ years, when the rates of the interest for successive years are $10\%$ , $14\%$ and $15\%$ respectively.

A
Rs. $23.073.60$ and Rs. $7,073.60$

B
Rs. $23.073.60$ and Rs. $7,873.60$

C
Rs. $23.873.60$ and Rs. $7,073.60$

D
Rs. $28.073.60$ and Rs. $7,073.60$

Solution

Int-rest amt after one year = $\dfrac{16000\times 10}{100}= 1600$ Rs

C.A after one year $=16000+1700=17600$ Rs

Intrest after two year = $\dfrac{17600\times 14}{100}= 2464$

C.A after two years $=17600+2464=20064$ Rs

Intrest after thrree year = $\dfrac{20064\times 15}{100}= 3009.60$

C.A after three years $=20064+3009.60=23073.60$ Rs

intrest after three year $=23073.60-16000=7073.60$ Rs
Question 5
1 / -0

The value of an article which was purchased $2$ years ago, depreciates at $12$ % per annum. If its present value is Rs . $9680$ , the price at which it was purchased is:

A
Rs. $10,000$

B
Rs. $12,500$

C
Rs. $14,575$

D
Rs. $16,250$

Solution

Given, $A=$ Rs. $9680,T=2$ years, $R=12\%$
$\because A = P\left (1 - \displaystyle \frac{R}{100} \right)$
$9680 = P \left(1 - \displaystyle \frac{12}{100} \right)^{2}$
$9680=P\left(\dfrac{88}{100}\right)^2$
$P = 9680 \times \displaystyle \frac{25}{22} \times \frac{25}{22}$
$=$ Rs. $12,500$
Question 6
1 / -0

Mohan lent some amount of money at $9\%$ simple interest and an equal amount of money at $10\%$ simple interest each for $2$ years. If his total interest was Rs. $760$ , what amount was lent in each case?

A
Rs. $1700$

B
Rs. $1800$

C
Rs. $1900$

D
Rs. $2000$

Solution

Let the amount lent in each case be Rs. $x$
$\Rightarrow \dfrac{x\times9\times2}{100}+\dfrac{x\times10\times2}{100}=760$
$\Rightarrow \dfrac{18x}{100}+\dfrac{20x}{100}=760$
$\Rightarrow\;38x=76000$
$\Rightarrow\;x=2000$
Question 7
1 / -0

Arun borrowed a sum of money from Jayant at the rate of $8\%$ simple interest for the first four years, $10\%$ p.a. for the next $6$ years and $12\%$ p.a. beyond $10$ years. If he pays a total of Rs. $12160$ as interest only at the end of $15$ years, how much money did he borrow?

A
Rs. $12000$

B
Rs. $10000$

C
Rs. $8000$

D
Rs. $9000$
Question 8
1 / -0

A person lent a certain sum of money at $4\%$ simple interest and in $5$ years, the interest amounted to Rs. $520$ less than the sum lent. The sum lent was

A
Rs. $.600$

B
Rs. $650$

C
Rs. $700$

D
Rs. $750$

Solution

Let the sum lent be $Rs. x$

The interest in $5$ years $=\dfrac{x\times 4\times 5}{100}$

Given: $\dfrac{x\times4\times5}{100}=x-520$

$\Rightarrow \dfrac{x}{5}=x-520$

$\Rightarrow x-\dfrac{x}{5}=520$

$\Rightarrow \dfrac{4x}{5}=520$

$\Rightarrow 4x=520\times 5$

$\Rightarrow x=\dfrac{520\times 5}{4}$

$\Rightarrow\;x=$ Rs. $650$

Therefore, the sum lent is Rs. $650$
Question 9
1 / -0

The cost of a vehicle is Rs. $1,75,000$ . If its value depreciates at the rate of $20$ % per annum, then the total depreciation after $3$ years will be:

A
Rs. $86,400$

B
Rs. $82,500$

C
Rs. $84,500$

D
Rs. $85,400$

Solution

Value of the vehicle after 3 years
$= 1,75,000 \times \left(1 - \displaystyle \frac{20}{100} \right)^{3}$
$= 1,75,000 \times \displaystyle \frac{4}{5} \times \frac{4}{5} \times \frac{4}{5}$
= Rs. 89, 600
$\therefore$ Total depreciation = 1, 75, 000 - 89, 600
$= Rs. 85,400$
Question 10
1 / -0

Find the compound interest by using simple interest approach for Rs 5000 for 3 years at 8% per annum compounded annnually.

A
$1298.56$

B
$1289.00$

C
$1.200.89$

D
None of these

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Basics of Financial Mathematics Test 9

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Question 1

Rs.907.50Rs. 907.50Rs.907.50

Rs. 2482.50Rs.\ 2482.50Rs. 2482.50

Rs. 2582.50Rs.\ 2582.50Rs. 2582.50

Rs. 982.50Rs.\ 982.50Rs. 982.50

Solution

Question 2

43.21%43.21 \%43.21%

31.15%31.15 \%31.15%

23.14%23.14 \%23.14%

18.34%18.34 \%18.34%

Solution

Question 3

Rs. 6,945.75 and Rs. 945.75

Rs. 6,845.75 and Rs. 945.75

Rs. 6,945.75 and Rs. 945.85

Rs. 6,945.75 and Rs. 945.70

Solution

Question 4

Rs. 23.073.6023.073.6023.073.60 and Rs. 7,073.607,073.607,073.60

Rs. 23.073.6023.073.6023.073.60 and Rs. 7,873.607,873.607,873.60

Rs. 23.873.6023.873.6023.873.60 and Rs. 7,073.607,073.607,073.60

Rs. 28.073.6028.073.6028.073.60 and Rs. 7,073.607,073.607,073.60

Solution

Question 5

Rs. 10,00010,00010,000

Rs. 12,50012,50012,500

Rs. 14,57514,57514,575

Rs. 16,25016,25016,250

Solution

Question 6

Rs. 170017001700

Rs. 180018001800

Rs. 190019001900

Rs. 200020002000

Solution

Question 7

Rs. 120001200012000

Rs. 100001000010000

Rs. 800080008000

Rs. 900090009000

Question 8

Rs. .600.600.600

Rs. 650650650

Rs. 700700700

Rs. 750750750

Solution

Question 9

Rs. 86,40086,40086,400

Rs. 82,50082,50082,500

Rs. 84,50084,50084,500

Rs. 85,40085,40085,400

Solution

Question 10

1298.561298.561298.56

1289.001289.001289.00

1.200.891.200.891.200.89

None of these

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$Rs. 907.50$

$Rs.\ 2482.50$

$Rs.\ 2582.50$

$Rs.\ 982.50$

$43.21 \%$

$31.15 \%$

$23.14 \%$

$18.34 \%$

Rs. $23.073.60$ and Rs. $7,073.60$

Rs. $23.073.60$ and Rs. $7,873.60$

Rs. $23.873.60$ and Rs. $7,073.60$

Rs. $28.073.60$ and Rs. $7,073.60$

Rs. $10,000$

Rs. $12,500$

Rs. $14,575$

Rs. $16,250$

Rs. $1700$

Rs. $1800$

Rs. $1900$

Rs. $2000$

Rs. $12000$

Rs. $10000$

Rs. $8000$

Rs. $9000$

Rs. $.600$

Rs. $650$

Rs. $700$

Rs. $750$

Rs. $86,400$

Rs. $82,500$

Rs. $84,500$

Rs. $85,400$

$1298.56$

$1289.00$

$1.200.89$