Basics of Financial Mathematics Test 41

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Basics of Financial Mathematics Test 41

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Weekly Quiz Competition

Question 1
1 / -0

The present population of a city is 3,02,500. If the population increases by 10% every year, what was the population of the city two years ago?

A
$$2,80,000$$

B
$$2,75,000$$

C
$$2,48,000$$

D
$$2,50,000$$

Solution

Let the population before two years ago be $$x$$

Given the population increases by $$10\%$$

So increase in population after one year is $$\dfrac{10}{100}\times x=0.1 x$$

So population after one year is $$x+0.1 x=1.1 x$$

Increase in population after another one year is $$\dfrac{10}{100} \times 1.1 x=0.11 x$$

So population at present is $$1.1 x+0.11 x=1.21 x$$

But given population at present is $$3,02,500$$
$$\implies 1.21 x=302500$$

$$\implies x=\dfrac{302500}{1.21}=2,50,000$$

Population of city two years ago is $$2,50,000$$
Question 2
1 / -0

Depreciation means ___________________.

A
some fixed assets losing price with the passage of time

B
loss of value by the movable properties over the time of their use

C
loss in value of the equipment of a plant over time due to their use

D
gaining of value by a domestic currency in its foreign exchange market

Solution

This is 'wear and tear' in a fixed/immovable asset due to its use. For different assets, the rates of depreciation are announced by the countries, which may be similar or different among countries.
Question 3
1 / -0

Due to reduction of interest rate from 8% to 7.5% by bank, one man got Rs. 600 less as compared to early annual receipts. The amount deposited in the bank is _______________.

A
Rs. $$1, 00, 000$$

B
Rs. $$1, 50, 000$$

C
Rs. $$1, 20, 000$$

D
Rs. $$2, 00, 000$$

Solution
Question 4
1 / -0

XYZ Ltd. incurs a net loss of Rs. 5, 000 during are accounting years. Depreciation for the relevant year amount to Rs. 1000, preliminary expenses written off during the accounting years is Rs. 3, 000 and a loss of Rs. 4, 000 is due to sale of plant and mach ____________.

A
Rs. 3, 000

B
Rs. 2, 000

C
Rs. 5, 000

D
Rs. 4, 000
Question 5
1 / -0

The compound interest on $$₹\ 10000$$ at $$10 \%$$ per annum for $$3$$ years, compounded annually, is

A
1331

B
3310

C
3130

D
13310

Solution

Given:
Present value $$= ₹\ 10000$$
Interest rate $$= 10 \%$$ per annum
Time $$=3$$ years

To find the amount we have the formula,
Amount $$(A) = P (1+(r/100))^n$$
where $$P$$ is present value, $$r$$ is rate of interest, $$n$$ is time in years

Now substituting the values in above formula we get,
$$\therefore A = 10000 (1 +10/100)^3$$

$$\Rightarrow A = 10000 (11/10)^3$$
$$\Rightarrow A = 121 (10) (11)$$
$$\Rightarrow A = 1331 (10)$$
$$\Rightarrow A = ₹\ 13310$$

∴ Compound interest $$= A – P$$
$$= 13310 – 10000= ₹\ 3310$$
Question 6
1 / -0

Mark against the correct answer in the following:
A sum amounts to $$Rs.3605$$ in $$219$$ days at $$5\%$$ per annum. The sum is

A
$$Rs. 3250$$

B
$$Rs.3500$$

C
$$Rs.3400$$

D
$$Rs.3550$$

Solution

Let the required sum be $$Rs. x$$
Then,
$$SI = (P \times R \times T) / 100$$
$$Amount = P + SI$$
$$= x + [( x \times R \times T) / 100]$$
$$= x [ 1 + ((R \times T) / 100)]$$
$$x = Amount / [1 + ((R \times T) / 100)]$$
$$= 3605 / [1 + ((5 / 100) \times (219 / 365))]$$
$$= (3605 \times 36500) / 37595$$
$$x = Rs. 3500$$
Question 7
1 / -0

Radhika bought a car for $$Rs. 2,50,000$$. Next year its price decreased by $$10\%$$ and further next year it decreased by $$12\%$$. In the two years overall decrease per cent in the price of the car is

A
$$3.2\%$$

B
$$22\%$$

C
$$20.8\%$$

D
$$8\%$$

Solution

The correct answer is option $$(c)$$.
Cost price of the car $$=Rs. 2,50,000$$
It's price decreased next year by $$10\%$$
Now, the price$$=Rs.(2,50,000-\dfrac{10}{100}\times 2,50,000)=Rs. 2,25,000$$
Next year, further its price decreased by $$12\%$$
Now, the price$$=Rs.(2,25,000-2,25,000\times \dfrac{12}{100})=Rs. 1,98,000$$
Overall decreased percentage in two years,
$$=(\dfrac{2,50,000-1,98,000}{2,50,000}\times 100)\%=(\dfrac{52,000}{2,50,000}\times100)\%=20.8\%$$
Question 8
1 / -0

Four alternative options are given for each of the following statements.
Select the correct option.
(o) The principal that yields a simple interest of $$Rs. 1280$$ at $$16$$% per annum for $$8$$ months is

A
$$Rs. 10,000$$

B
$$Rs. 12,000$$

C
$$Rs. 12,800$$

D
$$Rs. 14,000$$

Solution
Question 9
1 / -0

The clan of Rs. 50,000 at 10% p.a. Compounded annually for a certain time period is Rs. 10,500. What is the time period?

A
2 years

B
5 years

C
7 years

D
4 years
Question 10
1 / -0

A man gave $$50\%$$ of his savings of $$84100$$ to his wife and divided the remaining sum among his two sons $$A$$ and $$B$$ of $$15$$ and $$13$$ years of age respectively. He divided it in such a way that each of his sons, when they attain the age of $$20$$ years would receive the same amount at $$5\%$$ compound interest per annum, the share of $$B$$ was -

A
$$20000$$

B
$$20500$$

C
$$22000$$

D
$$22500$$

Solution

Total savings $$ =$$ Rs. $$84100$$
Wife got $$= 50\%$$ of $$84100$$ $$=$$ Rs. $$42050$$
Let $$B$$ gets $$X$$, then $$A$$ will have $$ ( 42050 - X)$$
For $$A$$,
Rate $$ = 5\%$$
Time (n) = 5 years
Amount $$= P \left [1 + \dfrac{r}{100})\right]^n$$
Amount $$ = (42050 - X) \times \left [1 + (\dfrac{5}{100})\right]^5$$
Amount $$ = (42050 - X) \times 1.27$$ .........(i)
For $$B$$,
Time$$ = 7$$ years
Amount $$ = X \left [1 + \left (\dfrac{5}{100}\right)\right]^7$$
Amount $$ = 1.40X$$ ...........(ii)
According to question, we have
Amount of $$A =$$ Amount of $$B$$
$$(42050 - X)\times 1.27 = 1.40X$$
$$53403 - 1.27X = 1.40X$$
$$1.40X + 1.27X = 53403$$
$$2.67X = 53403$$
$$X = 20000$$
So, $$B$$ got Rs. $$20000$$.

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Basics of Financial Mathematics Test 41

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Question 1

$$2,80,000$$

$$2,75,000$$

$$2,48,000$$

$$2,50,000$$

Solution

Question 2

some fixed assets losing price with the passage of time

loss of value by the movable properties over the time of their use

loss in value of the equipment of a plant over time due to their use

gaining of value by a domestic currency in its foreign exchange market

Solution

Question 3

Rs. $$1, 00, 000$$

Rs. $$1, 50, 000$$

Rs. $$1, 20, 000$$

Rs. $$2, 00, 000$$

Solution

Question 4

Rs. 3, 000

Rs. 2, 000

Rs. 5, 000

Rs. 4, 000

Question 5

1331

3310

3130

13310

Solution

Question 6

$$Rs. 3250$$

$$Rs.3500$$

$$Rs.3400$$

$$Rs.3550$$

Solution

Question 7

$$3.2\%$$

$$22\%$$

$$20.8\%$$

$$8\%$$

Solution

Question 8

$$Rs. 10,000$$

$$Rs. 12,000$$

$$Rs. 12,800$$

$$Rs. 14,000$$

Solution

Question 9

2 years

5 years

7 years

4 years

Question 10

$$20000$$

$$20500$$

$$22000$$

$$22500$$

Solution

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