Basics of Financial Mathematics Test 22

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Basics of Financial Mathematics Test 22

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Weekly Quiz Competition

Question 1
1 / -0

Aman gave Rs.$$9500$$ as a loan to Megh at the rate of $$4\%$$ p.a. compounded yearly. Megh returned the amount after two years. Calculate the interest on the first year's interest.

A
$$380$$

B
$$270$$

C
$$15.2$$

D
$$40$$

Solution

$$P=9500,R=4,T=2$$ years

Interest in $$1$$ year$$=\cfrac { P\times R\times 1 }{ 100 } $$$$=\cfrac { 9500\times 4 }{ 100 } $$$$=380$$

Interest on interest$$=\cfrac { 380\times 4\times 1 }{ 100 } $$$$=15.2$$
Question 2
1 / -0

The bank offers senior citizens intrest at the rate $$9\%$$ p.a compounded yearly on a fixed deposit. What interest will be received at the end of $$5$$ years if Rs.$$10,000$$ are deposited. Calculate by the method of simple interest.

A
$$5386.23$$

B
$$5500.23$$

C
$$6523.65$$

D
$$4367.78$$

Solution

$$P=10000,R=9,T=5$$ yrs
Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 10000\times 9\times 1 }{ 100 } $$
$$=900$$
$$P'=(900+10000)$$
Interest in $$2$$nd year$$=\cfrac { 10900\times 9\times 1 }{ 100 } =981$$
Interest in $$3$$rd year$$=\cfrac { 11881\times 9\times 1 }{ 100 }$$
$$=1069.29$$
Interest in $$4$$th year$$=\cfrac { 12950.29\times 9\times 1 }{ 100 }$$
$$=1165.5261$$
Interest in $$5$$th year$$=\cfrac { 14115.81\times 9\times 1 }{ 100 }$$
$$=1270.42$$
Total interest$$=900+981+1069.29+1165.52+1270.42$$
$$=5386.23$$
Question 3
1 / -0

A bank pays interest at the rate of $$8\%$$ per annum compounded yearly. Find the interest by simple interest method if $$Rs.\ 8000$$ was deposited for $$3$$ years.

A
$$Rs.\ 1000$$

B
$$Rs.\ 2077.7$$

C
$$Rs.\ 2000$$

D
$$Rs.\ 3456$$

Solution

$$P=Rs.\ 8000,R=8$$%, Time period$$=3$$ years

Interest in $$1$$st year $$=\cfrac { P\times R\times T }{ 100 } $$
$$=\cfrac { 8000\times 8\times 1 }{ 100 } $$
$$=Rs.\ 640$$

Principal amount for $$2$$nd year will be,
$$P'=P+640$$
$$=Rs.\ 8000+Rs.\ 640$$
$$=Rs.\ 8640$$

Interest in $$2$$nd year$$=\cfrac { 8640\times 8 }{ 100 } $$
$$=Rs.\ 691.2$$

Principal amount for $$2$$nd year will be,
$$P''=P'+691.2$$
$$=Rs.\ 8640+Rs.\ 691.2$$
$$=Rs.\ 9331.2$$

Interest in $$3$$rd year $$=\cfrac { 9331.2\times 8 }{ 100 } $$
$$=Rs.\ 746.5$$

So, total interest $$=640+691.2+746.5$$
$$=Rs.\ 2077.69$$
$$\approx Rs.\ 2077.7$$
Question 4
1 / -0

A businessman borrowed the Rs.$$45$$ lakh for two years at the rate $$2.5\%$$ p.a. compounded annually. Calculate the compound interest by simple interest method.

A
$$2,23000$$

B
$$2,27,812.5$$

C
$$5,65,563$$

D
$$2,00,000$$

Solution

$$\Rightarrow$$ Here, Principal amount for first year is $$Rs.45,00,000$$ and $$R=2.5\%$$.
$$\Rightarrow$$ Interest for first year = $$\dfrac{4500000\times 2.5}{100}=Rs.1,12,500$$

$$\Rightarrow$$ Principal amount for second year = $$Rs.4500000+Rs.112500=Rs.46,12,500$$

$$\Rightarrow$$ Second year interest = $$\dfrac{4612500\times 2.5}{100}=Rs.1,15,312.5$$

$$\Rightarrow$$ Total interest for 2 yeras = $$Rs.1,12,500+Rs.1,15,312.5=Rs.2,27,812.5$$
Question 5
1 / -0

The population of a town $$3$$ years ago was Rs. $$50,000$$.If the population in these three years has increased at the rate of $$10\%,15\%$$ and $$8\%$$ respectively, find the present population.

A
Rs. $$68,210$$

B
Rs. $$68,310$$

C
Rs. $$68,410$$

D
Rs. $$68,510$$

Solution

Let $$P=.50,000$$ and
$$R_1=10\%,\\ R_2=15\%,\\ R_3=8\%$$.
Present population = $$P\times \left (1+\dfrac{R_1}{100}\right)\left (1+\dfrac{R_2}{100}\right)\left (1+\dfrac{R_3}{100}\right)$$
On substituiting the given values,
Present population $$=$$ $$50000\times \left (1+\dfrac{10}{100}\right)\times \left (1+\dfrac{15}{100}\right)\times \left (1+\dfrac{8}{100}\right)$$
$$=$$ $$50000\times \dfrac{11}{10}\times \dfrac {23}{20}\times \dfrac{27}{25} =68310$$
Therefore, present population $$=$$ $$68310$$.
Question 6
1 / -0

A man lends Rs. $$12,500$$ at $$12$$% for the first year, at $$15$$% for the second year and at $$18$$% for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. for the first year and the compound interest for the third year.

A
$$\text{Rs }1,498$$

B
$$\text{Rs }1,598$$

C
$$\text{Rs }1,298$$

D
$$\text{Rs }1,398$$
Question 7
1 / -0

In what time will Rs. 4000 amount to Rs. 5324 at 10% per annum compound interest?

A
$$1$$ years

B
$$2$$ years

C
$$3$$ years

D
$$4$$ years

Solution

Given that, $$P=Rs.\ 4000,\,A=Rs.\ 5324$$ and $$R=10\%$$
Let the time be $$T$$ years
We know that, for compound interest,
$$A=P\times \left(1+\dfrac{R}{100}\right)^T$$

$$\therefore \ 5324=4000\times \left(1+\dfrac{10}{100}\right)^T$$

$$\Rightarrow$$ $$\dfrac{5324}{4000}=\left(1+\dfrac{1}{10}\right)^T$$

$$\Rightarrow$$ $$\dfrac{1331}{1000}=\left(\dfrac{11}{10}\right)^T$$

$$\Rightarrow$$ $$\left(\dfrac{11}{10}\right)^3=\left(\dfrac{11}{10}\right)^T$$

$$\therefore$$ $$T=3\,years$$.

Hence, $$Rs.\ 4000$$ will amount to $$Rs.\ 5324$$ at $$10\%$$ per annum in $$3$$ years.
Question 8
1 / -0

What amount will sum up to Rs. $$6,655$$ at $$10$$% p.a. in CI in $$3$$ years?

A
$$4,000$$

B
$$5,000$$

C
$$6,000$$

D
$$5,500$$

Solution

$$\Rightarrow$$ We have, $$A=Rs.6,655,\,R=10\%$$ and $$T=3\,years$$
$$\Rightarrow$$ $$A=P\times (1+\dfrac{R}{100})^T$$

$$\Rightarrow$$ $$6655=P\times (1+\dfrac{10}{100})^3$$

$$\Rightarrow$$ $$6655=P\times (\dfrac{11}{10})^3$$

$$\Rightarrow$$ $$P=\dfrac{6655\times 1000}{1331}=Rs.5000$$
Question 9
1 / -0

What sum of money will amount to Rs. $$31,944$$ in three years at $$10$$% per annum compounded yearly?

A
Rs.$$22,000$$

B
Rs.$$27,000$$

C
Rs.$$24,000$$

D
Rs.$$25,000$$

Solution

$$\Rightarrow$$ Here, we have $$A=Rs.31,944,\,T=3\,years$$ and $$R=10\%$$.
$$\Rightarrow$$ $$A=P\times (1+\dfrac{R}{100})^T$$

$$\Rightarrow$$ $$31,944=P\times (1+\dfrac{10}{100})^3$$

$$\Rightarrow$$ $$31,944=P\times (\dfrac{11}{10})^3$$

$$\Rightarrow$$ $$31,944=P\times \dfrac{1331}{1000}$$

$$\Rightarrow$$ $$P=\dfrac{31,944\times 1000}{1331}$$

$$\therefore$$ $$P=Rs.24,000$$.
Question 10
1 / -0

A sum of $$Rs.\ 15,000$$ is invested for $$3$$ years at $$10 \%$$ per annum compound interest. Calculate the interest for the second year.

A
$$Rs.\ 1,680$$

B
$$Rs.\ 1,650$$

C
$$Rs.\ 1,710$$

D
$$Rs.\ 1,640$$

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Basics of Financial Mathematics Test 22

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Basics of Financial Mathematics Test 22

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SHARING IS CARING

Question 1

$$380$$

$$270$$

$$15.2$$

$$40$$

Solution

Question 2

$$5386.23$$

$$5500.23$$

$$6523.65$$

$$4367.78$$

Solution

Question 3

$$Rs.\ 1000$$

$$Rs.\ 2077.7$$

$$Rs.\ 2000$$

$$Rs.\ 3456$$

Solution

Question 4

$$2,23000$$

$$2,27,812.5$$

$$5,65,563$$

$$2,00,000$$

Solution

Question 5

Rs. $$68,210$$

Rs. $$68,310$$

Rs. $$68,410$$

Rs. $$68,510$$

Solution

Question 6

$$\text{Rs }1,498$$

$$\text{Rs }1,598$$

$$\text{Rs }1,298$$

$$\text{Rs }1,398$$

Question 7

$$1$$ years

$$2$$ years

$$3$$ years

$$4$$ years

Solution

Question 8

$$4,000$$

$$5,000$$

$$6,000$$

$$5,500$$

Solution

Question 9

Rs.$$22,000$$

Rs.$$27,000$$

Rs.$$24,000$$

Rs.$$25,000$$

Solution

Question 10

$$Rs.\ 1,680$$

$$Rs.\ 1,650$$

$$Rs.\ 1,710$$

$$Rs.\ 1,640$$

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