Basics of Financial Mathematics Test 4

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Basics of Financial Mathematics Test 4

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Weekly Quiz Competition

Question 1
1 / -0

Determine the principal when time $$= 2$$ years, interest $$=$$ Rs.$$ 1000$$; rate $$= 2\%$$ p.a.

A
$$10000$$

B
$$20000$$

C
$$15000$$

D
$$25000$$

Solution

Here, time $$=2$$ years, interest $$=$$ Rs. $$1000$$, rate $$=2\%$$ p.a.
We know $$S.I.=\dfrac{P\times R\times T}{100}$$
$$\Rightarrow$$ $$1000=\dfrac{P\times 2\times 2}{100}$$
$$\Rightarrow$$ $$P=\dfrac{1000\times 100}{4}$$
$$\Rightarrow$$ $$P=$$ Rs. $$25,000$$
Question 2
1 / -0

Calculate the principal when time $$= 4$$ years, interest $$=$$ Rs. $$4000$$; rate = $$10$$% p.a

A
$$5,000$$

B
$$10,000$$

C
$$15,000$$

D
$$20,000$$

Solution

$$\Rightarrow$$ Here $$I=Rs.4000,\,R=10\%,\,T=4\,years$$

$$\Rightarrow$$ $$P=\dfrac{I\times 100}{R\times T}$$

$$\Rightarrow$$ $$P=\dfrac{4000\times 100}{10\times 4}$$

$$\Rightarrow$$ $$P=Rs.10,000$$
Question 3
1 / -0

In what time will Rs, $$15,000$$ yield Rs. $$4965$$ as compound interest at $$10$$% per year compounded annually?

A
$$3$$ years

B
$$2$$ years

C
$$1$$ years

D
$$4$$ years

Solution

Interest for the first year
$$=\cfrac{1500\times 10\times 1}{100}$$
$$=$$ Rs $$1500$$
Amount after the first year $$=$$ Rs $$15000+1500$$
$$=$$ Rs $$ 16500$$
Interest for the second year
$$=$$ $$\cfrac{16500\times 10\times 1}{100}$$
$$=$$ Rs $$1650$$
Amount after the third year
$$=$$ $$\cfrac{18150\times 10\times 1}{100}$$
$$=$$ Rs $$1815$$
Final amount $$= $$ Rs $$18150+1815$$
$$=$$ Rs $$19965$$
Compound interest $$=$$ Rs $$19965-15000$$
$$=$$ Rs $$4965$$
Required time $$= 3$$ years
Question 4
1 / -0

Find rate, when principal = Rs. $$30,000$$; interest = Rs. $$900$$; time = $$3$$ years.

A
$$1$$%

B
$$2$$%

C
$$4$$%

D
$$5$$%

Solution

using simple interest formula

Interest $$=$$ Principal $$\times$$ rate $$\times$$ time

Given:
Principal $$=$$ Rs. $$30000$$
Rate $$= r$$
Time $$= 3$$ years
Interest $$=$$ Rs. $$900$$
By substituting the given values in the formula,

$$\Rightarrow 900 = 30000 \times r \times 3$$

$$\Rightarrow r = \dfrac{900}{90000}$$

$$\therefore r = 0.01$$ or $$1\%$$
Question 5
1 / -0

Calculate the principal when time $$= 10$$ years, interest $$=$$ Rs. $$4000$$; rate = $$5\%$$ p.a.

A
$$5000$$

B
$$6000$$

C
$$7000$$

D
$$8000$$

Solution

Here, time $$=10$$ years, interest $$=$$ Rs. $$4000$$, rate $$=5\%$$ p.a.
We know $$S.I.=\dfrac{P\times R\times T}{100}$$
$$\Rightarrow$$ $$4000=\dfrac{P\times 5\times 10}{100}$$
$$\Rightarrow$$ $$P=\dfrac{4000\times 100}{50}=$$ Rs. $$8000$$
$$\Rightarrow$$ $$\text{Principal}=$$ Rs. $$8000.$$
Question 6
1 / -0

__________ is calculated on both the amount borrowed and any previous interest.

A
simple interest

B
annual interest

C
compound interest

D
complex interest

Solution

$$\text{Compound interest}$$ is calculated on both the amount borrowed and any previous interest.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
$$\Rightarrow$$ $$C.I.=A-P$$
Question 7
1 / -0

A sum of money at C.I amounts to thrice itself in $$6$$ years.Find in how many years will it be $$9$$ times itself

A
$$5$$

B
$$6$$

C
$$7$$

D
$$12$$

Solution

Let the principle be $$x$$.

According to the question,
$$3x=x\left(1+\dfrac{R}{100}\right)^6$$

$$3=\left(1+\dfrac{R}{100}\right)^6$$ $$..........(1)$$

Now,
Let it is $$9$$ times in $$T$$ years, then
$$9x=x\left(1+\dfrac{R}{100}\right)^T$$

$$3^2=\left(1+\dfrac{R}{100}\right)^T$$

From equation $$(1)$$, we get
$$\left(\left(1+\dfrac{R}{100}\right)^2\right)^6=\left(1+\dfrac{R}{100}\right)^T$$

$$\left(1+\dfrac{R}{100}\right)^{12}=\left(1+\dfrac{R}{100}\right)^T$$

On comparing both sides, we get
$$T=12\ years$$

Hence, this is the answer.
Question 8
1 / -0

Which interest is computed on the sum of an original principal and accrued interest?

A
Simple interest

B
Annual interest

C
Compound interest

D
Complex interest

Solution

$$\text{Compound interest}$$ is computed on sum of original principal and accrued interest.
Conversely, compound interest accrues on the principal amount and the accumulated interest of previous periods; it includes interest on interest, in other words.
It is calculated by multiplying the principal amount by the annual interest rate raised to the number of compound periods, and then minus the reduction in the principal for that year.
$$\Rightarrow$$ $$C.I.=P\left (1+\dfrac{R}{100}\right)^T-P$$
Question 9
1 / -0

A finance company declares that, with compound interest rate, a sum of money deposited by anyone will become $$8$$ times in three years. if the same amount is deposited at the same compound-rate of interest, then in how many years it will become $$128$$ times?

A
$$4$$

B
$$5$$

C
$$6$$

D
$$7$$

Solution

In three years.a sum of money deposited by anyone will become $$=2^3=8$$times
Therefore , to make sum of money $$128$$ times , then $$2^7=128$$, it will occcur in $$7$$ years.
Question 10
1 / -0

Determine the principal when time $$= 4$$ years, interest = Rs.$$ 1000$$; rate $$= 2$$% p.a.

A
$$10,000$$

B
$$12,500$$

C
$$15,000$$

D
$$20,000$$

Solution

$$\Rightarrow$$ Here $$I=Rs.1000,\,R=2\%,\,T=4\,years$$

$$\Rightarrow$$ $$P=\dfrac{I\times 100}{R\times T}$$

$$\Rightarrow$$ $$P=\dfrac{1000\times 100}{2\times 4}$$

$$\Rightarrow$$ $$P=Rs.12,500$$

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Basics of Financial Mathematics Test 4

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Question 1

$$10000$$

$$20000$$

$$15000$$

$$25000$$

Solution

Question 2

$$5,000$$

$$10,000$$

$$15,000$$

$$20,000$$

Solution

Question 3

$$3$$ years

$$2$$ years

$$1$$ years

$$4$$ years

Solution

Question 4

$$1$$%

$$2$$%

$$4$$%

$$5$$%

Solution

Question 5

$$5000$$

$$6000$$

$$7000$$

$$8000$$

Solution

Question 6

simple interest

annual interest

compound interest

complex interest

Solution

Question 7

$$5$$

$$6$$

$$7$$

$$12$$

Solution

Question 8

Simple interest

Annual interest

Compound interest

Complex interest

Solution

Question 9

$$4$$

$$5$$

$$6$$

$$7$$

Solution

Question 10

$$10,000$$

$$12,500$$

$$15,000$$

$$20,000$$

Solution

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