Basics of Financial Mathematics Test 17

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Basics of Financial Mathematics Test 17

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Weekly Quiz Competition

Question 1
1 / -0

Find the compound interest on Rs. $6400$ for $2$ years, compounded annually at $\dfrac{15}{2}\%$ per annum.

A
$996$

B
$986$

C
$976$

D
$966$

Solution

$\Rightarrow$ $P=Rs.6400,\, n=2\,years,\, R=\dfrac{15}{2}\%$
$\Rightarrow$ $A=P(1+\dfrac{R}{100})^n$

$\Rightarrow$ $A=6400(1+\dfrac{15}{2\times 100})^2$

$\Rightarrow$ $A=6400\times \dfrac{215}{200}\times \dfrac{215}{200}$
$\Rightarrow$ $A=Rs.7,396$
$\Rightarrow$ $Compound\, interest = A-P$
$\Rightarrow$ $Compound\, Interest =Rs. 7,396-Rs.6,400=Rs.996$
Question 2
1 / -0

If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

A
$$ $ 20,000$$

B
$$ $ 15,000$$

C
$$ $ 12,000$$

D
$$ $ 10,000$$

E
$$ $ 9,000$$

Solution

$\Rightarrow$ We have given that $r$ = Percent interest.
$\Rightarrow$ We are also given that an investment with double in approximately $70/r$ years.
$\Rightarrow$ We are told to invest $\$5,000$ at $8\%$ for 18 years.
$\Rightarrow$ Put $r=8$
$\Rightarrow$ So, $\dfrac{70}{8}$ is about $9\,years$ , meaning investment will double in $9\,years$ .
$\Rightarrow$ In the first 9 years, $\$5,000$ doubles to $\$10,000$
$\Rightarrow$ In the next 9 years, $\$10,000$ doubles to $\$20,000$
$\therefore$ The approximate total amount of investment 18 years later, when Pat is ready for college is $\$20,000$ .
Question 3
1 / -0

The present population of town is $12500$ and it is increasing at the rate of $8\%$ per annum. What will be the population of town after two years?

A
$14000$

B
$12500$

C
$14580$

D
$25000$

Solution

Given, present population of town $=12500, R=8\%$
Therefore, population after $2$ years $=12500\times\begin{Bmatrix}1+\dfrac{8}{100}\end{Bmatrix}^2$
$=12500\times\begin{Bmatrix}\dfrac{108}{100}\end{Bmatrix}^2$
$=14580$
Question 4
1 / -0

Find the interest for the principal Rs. $4110$ at the rate of $6\%$ for $2$ years.

A
$343.50$

B
$493.20$

C
$460.19$

D
$531.12$

Solution

Simple interest, $I =$ $\dfrac{PRT}{100}$
Where, $P$ is the principal $=4110$
$R$ is the rate $=6\%$
$T$ is the time period $=2$ years
$I =$ $\dfrac{4110\times 6\times 2}{100}$
$I =$ Rs. $493.20$
Question 5
1 / -0

John earned Rs. $100$ as simple interest on Rs. $600$ for $6$ months. Find the annual rate of interest.

A
$11.11\%$

B
$22.22\%$

C
$33.33\%$

D
$44.44\%$

Solution

Given, Simple interest $=$ Rs. $100$ , Principal $=$ Rs. $600$ and period $6$ months
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$R =$ $\dfrac{100\times 100}{600\times 0.5}$
$R = 33.33\%$
Therefore, the annual rate of interest is $33.33\%$ .
Question 6
1 / -0

Identify the two statements by which the principal sum can be calculated?
P : The sum amounts to Rs. $690$ in $3$ yrs at Simple Interest.
Q : The sum amounts to Rs. $750$ in $5$ yrs at Simple interest.
R : The rate of interest is $5\%$ per annum.

A
P & Q will give the answer

B
R & Q will give the answer

C
P & R will give the answer

D
Any two will give the answer

Solution

Any two of three will give the answer because if amount, rate and number of years are given, we can easily find out the principal sum.
Question 7
1 / -0

Priya invested a certain amount of money and got back an amount of Rs. $15000$ . If the bank paid an interest of Rs. $5000$ , what is the amount Priya invested?

A
$5000$

B
$8000$

C
$15000$

D
$10000$

Solution

Amount $=$ Rs. $15000$
Simple interest $=$ Rs. $5000$
Principal $=$ Amount $-$ simple interest
$= 15000 - 5000$
Principal $= 10000$
Therefore, priya invested Rs. $10000$ .
Question 8
1 / -0

In a culture, the present bacteria count was found as $67,60,000$ . It was found that the number was increased by $4\%$ per hour. Find the number of hours before which the bacteria count was $62,50,000$ .

A
$1$ hr

B
$2$ hr

C
$3$ hr

D
$4$ hr

Solution

Let the number of years be $n$
$\Rightarrow 67,60,000=62,50,000 \left [1+\dfrac{4}{100}\right]^n$
$\Rightarrow \dfrac{676}{625}=[1+\dfrac{1}{25}]^n$
$\Rightarrow \left [\dfrac{26}{25}\right]^2=\left [\dfrac{26}{25}\right]^n$
$n=2$ hrs
Thus, the number of hours are $2$ .
Question 9
1 / -0

The present population of a city is $18522000$ . If it has been increased at the rate of $5\%$ per annum, find the population(approx) after $3$ years.

A
$2522200$

B
$16000000$

C
$21441530$

D
$252200$

Solution

Given, Principal amount $18522000$ , rate of interest $=5\%$ and period $=3$ years
Total Population $=18522000\left [1+\dfrac{5}{100}\right]^3$
$=18522000\left [1+\dfrac{1}{20}\right]^3$
$=21441530$ (approx)
Question 10
1 / -0

Find rate, when principal $=$ Rs. $3000$ ; interest $=$ Rs. $400$ ; time $= 3$ years.

A
$1.11\%$

B
$2.22\%$

C
$3.33\%$

D
$4.44\%$

Solution

Given, Principal $=$ Rs. $3000$ , interest $=$ Rs. $400$ , time $=3$ years
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$R =$ $\dfrac{400\times 100}{3000\times 3}$
$R = 4.44\%$

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Basics of Financial Mathematics Test 17

Result

Basics of Financial Mathematics Test 17

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SHARING IS CARING

Question 1

996996996

986986986

976976976

966966966

Solution

Question 2

$$ $ 20,000$$

$$ $ 15,000$$

$$ $ 12,000$$

$$ $ 10,000$$

$$ $ 9,000$$

Solution

Question 3

140001400014000

125001250012500

145801458014580

250002500025000

Solution

Question 4

343.50343.50343.50

493.20493.20493.20

460.19460.19460.19

531.12531.12531.12

Solution

Question 5

11.11%11.11\%11.11%

22.22%22.22\%22.22%

33.33%33.33\%33.33%

44.44%44.44\%44.44%

Solution

Question 6

P & Q will give the answer

R & Q will give the answer

P & R will give the answer

Any two will give the answer

Solution

Question 7

500050005000

800080008000

150001500015000

100001000010000

Solution

Question 8

111 hr

222 hr

333 hr

444 hr

Solution

Question 9

252220025222002522200

160000001600000016000000

214415302144153021441530

252200252200252200

Solution

Question 10

1.11%1.11\%1.11%

2.22%2.22\%2.22%

3.33%3.33\%3.33%

4.44%4.44\%4.44%

Solution

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Question Analysis

My Perfomance

Score

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Rank

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$996$

$986$

$976$

$966$

$14000$

$12500$

$14580$

$25000$

$343.50$

$493.20$

$460.19$

$531.12$

$11.11\%$

$22.22\%$

$33.33\%$

$44.44\%$

$5000$

$8000$

$15000$

$10000$

$1$ hr

$2$ hr

$3$ hr

$4$ hr

$2522200$

$16000000$

$21441530$

$252200$

$1.11\%$

$2.22\%$

$3.33\%$

$4.44\%$