Basics of Financial Mathematics Test 34

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Basics of Financial Mathematics Test 34

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Question 1
1 / -0

An annuity is?

A
A fixed sum

B
Paid at regular intervals

C
Under certain stated conditions

D
All of the above

Solution

An annuity is
$$(1)$$A fixed sum
$$(2)$$ Paid at regular intervals
$$(3)$$Under certain stated conditions.
Question 2
1 / -0

Mrs. S deposited Rs. $$1,00,000$$ in a nationalized bank for $$3$$ years. If the rate of interest is $$7\%$$ p.a., Interest is compounded annually. Calculate the amount at the end of third year (i.e., Principal $$+$$ compound interest)

A
$$1,22,504.03$$

B
$$1,02,504.30$$

C
$$1,22,505.30$$

D
$$1,22,405.30$$

Solution

Interest for the$$1^{ st }$$ year $$= Rs.\dfrac { 100000\times 1\times 7 }{ 100 } =Rs. 7000$$

Amount after the$$1^{ st }$$ year $$= Rs. 100000 + Rs.7000= Rs. 107000$$

Interest for the $$2^{nd}$$ year $$= Rs.\dfrac{107000\times 1\times 7}{100} = Rs.7490$$

Amount after the $$2^{nd}$$ year $$= Rs. 107000 + Rs. 7490 = Rs. 114490$$

Interest for the$$3^{ rd }$$ year $$= Rs. \dfrac { 114490\times 1\times 7 }{ 100 } = Rs. 8014.3$$

$$\therefore$$ Amount at the end of the $$3^{rd}$$ year $$= Rs. 114490+ Rs. 8014.3= Rs. 122504.30$$
Question 3
1 / -0

A sum of Rs. $$1,200$$ becomes Rs. $$1,323$$ in $$2$$ years at compound interest compounded annually. Find the rate per cent.

A
$$8\%$$

B
$$7\%$$

C
$$6\%$$

D
$$5\%$$

Solution

Let r% be rate per annum, then,
$$1323 = 1200(1 + \cfrac{r}{100})^2$$
$$\implies \cfrac{1323}{1200} = (1+\cfrac{r}{100})^2$$
$$\implies \sqrt{\cfrac{1323}{1200}} = (1+\cfrac{r}{100})$$
$$\implies 1.05 = (1+\cfrac{r}{100})$$
$$\implies \cfrac{r}{100} = 1.05 - 1 = 0.05$$
$$\implies r= 100 \times 0.05 = 5$$%
Question 4
1 / -0

Find the compound interest for Rs. $$1,000$$ for $$4$$ years at $$5\%$$ p.a. When the interest is compounded annually.

A
$$220$$

B
$$218$$

C
$$215$$

D
$$250$$

Solution

Interest for first year $$ =\cfrac{1000 \times 5 \times 1}{100} = ₹50$$
Amount after first year $$= 1000+50=₹1050$$
Interest for second year $$= \cfrac{1050 \times 5 \times 1}{100} = ₹52.5$$
Amount after second year $$= 1050+52.5=₹1102.5$$
Interest for third year $$= \cfrac{1102.5 \times 5 \times 1}{100} = ₹55.125$$
Amount after third year $$= 1102.5+55.125=₹1157.625$$
Interest for fourth year $$= \cfrac{1157.625 \times 5 \times 1}{100} = ₹57.88125$$
Amount after fourth year $$= 1157.625+57.88125=₹1215.50625$$
Compound interest $$=1215.50625 - 1000 = 215.50625 = ₹215$$
Question 5
1 / -0

Tanishka deposited Rs. $$50,000$$ in a bank for two years with the interest rate of $$5.5\%$$ p.a. How much interest would she earn?

A
$$6,000$$

B
$$5,250$$

C
$$55,500$$

D
$$5,500$$

Solution

$$ Interest = \cfrac{ 50000 \times 2 \times 5.5 }{100} = 5500$$
Question 6
1 / -0

The S.I. accrued on an amount of Rs. $$25,000$$ at the end of three years is Rs. $$7,500$$. What would be the C.I. accrued on the same amount at the same rate in the same period?

A
$$7,750$$

B
$$8,275$$

C
$$8,500$$

D
$$8,250$$

E
None of these

Solution

Apply the formula for simple interest

$$7500=\dfrac{25000\times R\times3}{100}$$

$$\implies R=\dfrac{7500}{250\times3}=10\%$$

Interest for the $$1$$st year$$=\dfrac{25000\times10\times1}{100}$$
$$=2500$$

Amount After the $$1$$st year$$=25000+$$$$2500$$
$$=27500$$
Interest for the $$2$$nd year$$=\dfrac{27500\times10\times1}{100}$$
$$=2750$$

Amount After the $$2$$nd year$$=27500+$$$$2750$$
$$=30250$$
Interest for the $$3$$rd year$$=\dfrac{30250\times10\times1}{100}$$
$$=3025$$

Amount After the $$3$$rd year$$=30250+$$$$3025$$
$$=33275$$

$$\therefore$$Compound Interest(CI)$$=33275-$$$$25000$$
$$=Rs.8275$$
Question 7
1 / -0

What will be the C.I. on a sum of Rs. $$25,000$$/- after $$3$$ years at the rate of $$12\%$$p.a?

A
Rs.$$35,123.2$$

B
$$15,200$$

C
Rs.$$10123.2$$

D
Rs.$$3,26,232$$

Solution

$$P=25000$$
$$T=3years$$
$$R=12\%pa$$
$$A=P(1+\frac{R}{100})^T$$
$$=>A=25000(1+\frac{12}{100})^3$$
$$=25000(\frac{28}{25})^3$$
$$=35123.2$$
$$I=A-P$$
$$=35123.2-25000$$
$$I$$$$=Rs.10123.2$$
Question 8
1 / -0

Which of the following is not an effect of simplification of procedural aspects in Taxation?

A
Improvement in tax compliance

B
Increased revenue generation for the Government

C
More work for Tax Authorities and Taxpayers

D
All of the above

Solution
Question 9
1 / -0

If $$P=Rs. 1,000$$, R$$=5\%$$, p.a., $$n=4$$; What is amount and CI?

A
Rs. $$1,215.50$$ & $$215.50$$

B
Rs. $$1,125$$ & $$125$$

C
Rs. $$2,115$$ & $$115$$

D
None of the above

Solution

$$P=Rs$$ $$1000$$, $$R=5\%$$ $$p.a.$$, $$n=4$$
Interest for the $$1^{st}$$ year $$= Rs$$ $$\cfrac{1000\times 5\times 1}{100}= Rs$$ $$50$$
Amount after $$1^{st}$$ year $$= Rs$$ $$1000+ Rs$$ $$50=Rs$$ $$1050$$
Interest for the $$2^{nd}$$ year $$= Rs$$ $$\cfrac{1050\times 5\times 1}{100}= Rs$$ $$52.5$$
Amount after $$2^{nd}$$ year $$= Rs$$ $$1050+ Rs$$ $$52.5=Rs$$ $$1102.5$$
Interest for the $$3^{rd}$$ year $$= Rs$$ $$\cfrac{1102.5\times 5\times 1}{100}= Rs$$ $$55.125$$
Amount after $$3^{rd}$$ year $$= Rs$$ $$1102.5+ Rs$$ $$55.125=Rs$$ $$1157.625$$
Interest for the $$4^{th}$$ year $$= Rs$$ $$\cfrac{1157.625\times 5\times 1}{100}= Rs$$ $$57.88125$$
Amount after $$1^{st}$$ year $$= Rs$$ $$1157.625+ Rs$$ $$57.88125=Rs$$ $$1215.50$$
$$\therefore$$ Compound Interest $$=Rs$$ $$1215.50-Rs$$ $$1000=Rs$$ $$215.50$$
Question 10
1 / -0

Which of the following is not part of the Taxation Reforms in 1991?

A
General policy for introduction of State-level VAT

B
Rationalisation of Excise Duties towards CENVAT concept

C
Reduction in the peak rate of Customs Duties

D
Increase in Customs, Excise and Sales Tax Rates

Solution

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Basics of Financial Mathematics Test 34

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Question 1

A fixed sum

Paid at regular intervals

Under certain stated conditions

All of the above

Solution

Question 2

$$1,22,504.03$$

$$1,02,504.30$$

$$1,22,505.30$$

$$1,22,405.30$$

Solution

Question 3

$$8\%$$

$$7\%$$

$$6\%$$

$$5\%$$

Solution

Question 4

$$220$$

$$218$$

$$215$$

$$250$$

Solution

Question 5

$$6,000$$

$$5,250$$

$$55,500$$

$$5,500$$

Solution

Question 6

$$7,750$$

$$8,275$$

$$8,500$$

$$8,250$$

None of these

Solution

Question 7

Rs.$$35,123.2$$

$$15,200$$

Rs.$$10123.2$$

Rs.$$3,26,232$$

Solution

Question 8

Improvement in tax compliance

Increased revenue generation for the Government

More work for Tax Authorities and Taxpayers

All of the above

Solution

Question 9

Rs. $$1,215.50$$ & $$215.50$$

Rs. $$1,125$$ & $$125$$

Rs. $$2,115$$ & $$115$$

None of the above

Solution

Question 10

General policy for introduction of State-level VAT

Rationalisation of Excise Duties towards CENVAT concept

Reduction in the peak rate of Customs Duties

Increase in Customs, Excise and Sales Tax Rates

Solution

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