Basics of Financial Mathematics Test 27

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Basics of Financial Mathematics Test 27

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Weekly Quiz Competition

Question 1
1 / -0

The time required for a sum of money to double at $$5$$% annum compounded continuously is (in years)

A
$$13.5$$

B
$$13.9$$

C
$$13$$

D
$$14.3$$

Solution

Amount after $$n$$ years compounded annually$$=P(1+\dfrac {r}{100})^n$$
Where, $$P$$ is the principal amount and $$r$$ is the interest rate per annum.

ie, $$2P=P(1+\dfrac {r}{100})^n\Rightarrow 2=(1+\dfrac {5}{100})^n=(1+\dfrac 1{20})^n$$

$$\Rightarrow \ln 2=n(\ln{\dfrac {21}{20}})\Rightarrow n=\dfrac {\ln 2}{\ln {21}-\ln {20}}\approx14.3$$

Option D is the correct answer.
Question 2
1 / -0

The value of a machine depreciates every year by $$5\%$$. If the present value of the machine be Rs. $$100,000$$, what will be its value after two years?

A
Rs. $$100,050$$

B
Rs. $$90, 250$$

C
Rs. $$99,250$$

D
Rs. $$99,000$$

Solution

current value of Machine $$=Rs. 100,00$$

After 1 year
value decreased by $$5 \%$$

value of Machine is
$$ Rs. 95 \% $$ $$of$$ $$100,000 $$

$$\Rightarrow \dfrac{95}{100} \times 100,000 = Rs. 95,000$$

After 2 years

again the value is decreased by $$5 \%$$ from previous year' s Value

Now value of Machine is
$$= 95 \% $$ $$of$$ $$95,000$$

$$= \dfrac{95}{100} \times 95,000$$

$$=0.95\times 95,000 $$

$$ = Rs. 90,250$$ is the value of machine at the of two years
Question 3
1 / -0

Which of the following asset does not depreciate?

A
Machinery and equipment

B
Motor Vehicles

C
Land

D
Furniture

Solution

Every asset is having a useful life based on its usage and nature. A predetermined rate is defined for charging a proportion of the value of the assets every year to profit & loss account which is known as depreciation.
The land is an asset that will have an unlimited useful life and does not depreciate because of its use.
Question 4
1 / -0

Equal sums of Rs.$$7200$$ were lent to Megha and Priya at $$5$$ $$\%$$ per annum for a period of $$4$$ years and $$5$$ years respectively. Find the difference of the interest paid by Megha and Priya.

A
Rs.$$140$$

B
Rs.$$560$$

C
RS.$$260$$

D
Rs.$$360$$

Solution

Simple interest on the sum $$P$$ at rate of interest $$R$$ for $$N$$ years is given as $$\dfrac{PNR}{100}$$
$$\text{Interest paid by Priya} = \dfrac{7200\times 5\times 5}{100}\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =Rs\ 1800$$

$$\text{Interest paid by Megha} = \dfrac{7200\times 4\times 5}{100}\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =Rs\ 1440$$

Difference $$= 1800-1440$$
$$=Rs\ 360$$
Hence, D is the right option.
Question 5
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 was _________.

A
Rs. $$86,400$$

B
Rs. $$82,500$$

C
Rs. $$84, 500$$

D
Rs. $$85,400$$

Solution

Cost of vehicle $$= 175000$$
Depreciation for first year $$= \dfrac{20}{100}\times175000=35000$$

Cost of vehicle after first year $$= 175000-35000=140000$$
Depreciation for second year $$= \dfrac{20}{100}\times140000 = 28000$$

Cost of vehicle after second year $$= 140000-28000=112000$$
Depreciation for third year $$= \dfrac{20}{100}\times112000 = 22400$$

Total depreciation after $$3$$ years $$= 35000+28000+22400 = 85400$$
Hence, the answer is Rs. $$85,400$$.
Question 6
1 / -0

_________ cost will still be incurred although a plant is shut down temporarily.

A
Cost of raw material

B
Advertising

C
Depreciation

D
Carriage

Solution

To have a true and fair view of profit & loss of the organization, depreciation of the assets has to be charged on the basis of their useful life. If a plant is shut down temporarily, there may be significant spoilage of material in the process, some significant damage to the plant. Due to some reasons like lack of demand, maintenance of plant, the plant is shut down for some time. The shutdown does not change the inherent technical nature of the plant. Hence depreciation has to be charged.
Question 7
1 / -0

The compound interest on Rs. $$100000$$ at $$20\%$$ per annum for $$2$$ years $$3$$ months, compound annually is ________.

A
Rs. $$151200$$

B
Rs. $$100000$$

C
Rs. $$51200$$

D
Rs. $$251200$$

Solution

Given, $$P=100000$$, $$r=0.2$$, $$n=2+\dfrac{1}{4}$$ (converting $$2$$ years $$3$$ months to years) $$=n=2.25$$
Interest is compounded anually,
For first year $$=100000\times 0.2\times 1=20000$$
For second year $$P_{new }= 120000$$
Interest $$=120000\times 0 .2\times 1=24000$$
For last $$0.02544$$ year, $$p_{new}=144000$$
Interest $$ = 144000\times 0.2\times 0.25=7200$$
New amount $$=144000+7200 = 151200$$
$$\text{Interest} = 151200+100000=51200$$
Question 8
1 / -0

Depreciation is provided on _________.

A
Current assets

B
Liquid assets

C
Fictitious assets

D
Fixed assets

Solution

Fixed assets are those assets that provide long term benefits to the organization and are not meant to be sold in the course of business. Hence these are recorded in the balance sheet. A portion of the cost of these assets is charged to the profit & loss account every year which is termed as depreciation.
Question 9
1 / -0

Depreciation is a charge against _______.

A
Profit

B
Assets

C
Company

D
Books of A/c

Solution

Depreciation is a reserve but is a charge against profit since it is created for the replacement of an asset. Hence, both reserves and provisions can arise as a charge against profits or as an appropriation out of profit, depending upon the nature of provision or reserve.
Question 10
1 / -0

The purpose of depreciation is to _____________.

A
Reduce fixed assets to market value each year

B
Save income tax and wealth tax

C
Reduce fixed assets to the standard value

D
Allocate the cost of fixed asset

Solution

The purpose of depreciation is to match the cost of a productive asset, that has a useful life of more than a year, to the revenues earned by using the asset. The asset's cost is usually spread over the years in which the asset is used.
Depreciation is an allocation process in order to achieve the matching principle.

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Basics of Financial Mathematics Test 27

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Basics of Financial Mathematics Test 27

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Question 1

$$13.5$$

$$13.9$$

$$13$$

$$14.3$$

Solution

Question 2

Rs. $$100,050$$

Rs. $$90, 250$$

Rs. $$99,250$$

Rs. $$99,000$$

Solution

Question 3

Machinery and equipment

Motor Vehicles

Land

Furniture

Solution

Question 4

Rs.$$140$$

Rs.$$560$$

RS.$$260$$

Rs.$$360$$

Solution

Question 5

Rs. $$86,400$$

Rs. $$82,500$$

Rs. $$84, 500$$

Rs. $$85,400$$

Solution

Question 6

Cost of raw material

Advertising

Depreciation

Carriage

Solution

Question 7

Rs. $$151200$$

Rs. $$100000$$

Rs. $$51200$$

Rs. $$251200$$

Solution

Question 8

Current assets

Liquid assets

Fictitious assets

Fixed assets

Solution

Question 9

Profit

Assets

Company

Books of A/c

Solution

Question 10

Reduce fixed assets to market value each year

Save income tax and wealth tax

Reduce fixed assets to the standard value

Allocate the cost of fixed asset

Solution

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