Tag: mathematics and statistics

Questions Related to mathematics and statistics

A sum of Rs.$12,000$ is invested for $3$ years at $18$ % per annum compound interest. Calculate the interest for the second year.

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $2500$

  2. $2525$

  3. $2550$

  4. $2575$

Show answer
Correct Option: C
Explanation:

Interest for first year  = $ \cfrac{12000 \times 1 \times 18}{100} = 2160$

Amount after first year = $ 12000+2160=14160$
Interest for second year =$ \cfrac{14160 \times 1 \times 18}{100} = 2550(approx)$ 

What sum of money will amount to Rs. $18873$ in three years at $19$% per annum compounded yearly?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $8000$

  2. $10000$

  3. $12000$

  4. $11200$

Show answer
Correct Option: D
Explanation:
$A=P(1+\cfrac{r}{100})^n$
$\implies18873=P(1+\cfrac{19}{100})^3\ \implies P=11199\approx 11200$
Hence sum$=Rs.11,200$.

A sum of Rs.$12,000$ is invested for $3$ years at $18$ % per annum compound interest. Calculate the interest for the third year.

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $2700$

  2. $2800$

  3. $2900$

  4. $3000$

Show answer
Correct Option: D
Explanation:

Interest for the first year =$ \cfrac{12000 \times 1 \times 18}{100} = 2160$

Amount after first year = $12000+2160 =14160$
Interest for second year =$ \cfrac{14160 \times 1 \times 18}{100} = 2550$
Amount after second year = $14160+2550 =16708.8$

Interest for third year =$ \cfrac{16708.8 \times 1 \times 18}{100} = 3000(approx)$

A sum of Rs.$25,000$ is invested for $3$ years at $20$ % per annum compound interest. Calculate the interest for the third year.

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $6000$

  2. $7200$

  3. $8400$

  4. $5000$

Show answer
Correct Option: B
Explanation:

Interest for the first year =$ \cfrac{25000 \times 1 \times 20}{100} = 5000$

Amount after first year = $25000+5000 =30000$
Interest for second year =$ \cfrac{30000 \times 1 \times 20}{100} = 6000$
Amount after second year = $30000+6000 =36000$

Interest for third year =$ \cfrac{36000 \times 1 \times 20}{100} = 7200(approx)$

The compound interest on $Rs. 64,000$ for $3$ years, compounded annually at $7.5$% per annum is

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $Rs. 14,400$

  2. $Rs. 15,705$

  3. $Rs. 15,507$

  4. $Rs. 15,075$

Show answer
Correct Option: C
Explanation:

$Principal = 64000$
$Rate = 7.5\% \,p.a$
$Time = 3 years$ 
$\text{Where r is the rate and t is the time.}$
$CI = 64000 (1 + 7.5/100)^3 - 64000$
$= 64000 (1 + 75/1000)^3 - 64000$
$= 64000 (1 + 3/40)^3 - 64000$
$= 64000 (43/40)^3 - 64000$
$= 64000 * 43/40 * 43/40 * 43/40 - 64000$
$= 43 * 43 * 43 - 64000$
$= 79507 - 64000$
$= 15507$
$\text{Hence CI will be 15507 rupees}$

If the amount is $2 \dfrac{1}{4}$ times the sum after 2 years at compound interest, the rate of interest, per annum is 

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. 25%

  2. 30%

  3. 40%

  4. 50%

Show answer
Correct Option: D
Explanation:

Interest is compounded annually,

So amount, $A=P\left ( 1+\dfrac{r}{100} \right )^{t}$

Where $P$ is Principal (or sum)
$t$ is time (in years)
$A$ is the amount, person will get after time $t$
and $r$ is rate of interest per annum

Here $A=2\dfrac{1}{4}P=\dfrac{9}{4}P$
and $t=2$ years

Now apply the formula,
$A=P\left ( 1+\dfrac{r}{100} \right )^{t}$

$\dfrac{9}{4}P=P\left ( 1+\dfrac{r}{100} \right )^{2}$

$\Rightarrow \dfrac{9}{4}=\left ( 1+\dfrac{r}{100} \right )^{2}$

Square root both sides,

$\dfrac{3}{2}=\left ( 1+\dfrac{r}{100} \right )$

$\dfrac{r}{100}=\dfrac{3}{2}-1=\dfrac{1}{2}$

$r=\dfrac{100}{2}=50$%

Find the money which when invested for $1.5$ years and compounded annually at the rate of $8$% per annum, amounts to Rs. $175.37.$

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $168.21$

  2. $156.13$

  3. $159.36$

  4. none

Show answer
Correct Option: B
Explanation:
$T=1.5$ ,$R=8\%$,Amount$=175.37$
we know that,
$A=P\left(1+\dfrac{R}{100}\right)^{T} $
$\implies175.37=P\left(1+\dfrac{8}{100}\right)^{1.5}$
$P=\dfrac{175.37}{1.12}=156.13$

Priyanka borrowed $Rs8,000$ at $12\%$ simple interest for $3$years and lent it to Renu for $3$ years at $15\%$ per annum compound interested, compounded annually, Priyanka's profit at the end of $3$ years is

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $Rs.2,880$

  2. $Rs.1,287$

  3. $Rs.4,167$

  4. none of these

Show answer
Correct Option: A

The compound interest on $Rs5,000$ at $4\%$ per annum for $2$ years compounded annually will be

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $Rs806$

  2. $Rs708$

  3. $Rs5,408$

  4. $Rs408$

Show answer
Correct Option: A

Calculate the amount and compound interest on Rs. $62,500$ for $1\frac{1}{2}$ years at 8% per annum compounded half yearly.

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. Amount =Rs. 70304, compound interest=Rs. 7804

  2. Amount =Rs. 70304, compound interest=Rs. 7404

  3. Amount =Rs. 70204, compound interest=Rs. 7804

  4. Amount =Rs. 70442, compound interest=Rs. 7804

Show answer
Correct Option: A
Explanation:

Here, Principal =Rs. 62,500
Rate =8% per annum =4% half year
Time =$1\frac{1}{2}$ years =3 half years
$Amount = P(1 +\frac{R}{100})^T$
$\therefore Amount =Rs.[62500\times {(1+\frac{4}{100})}^{3}]$
$Amount = \displaystyle(62500\times \frac{104}{100}\times \frac{104}{100}\times \frac{104}{100}) =Rs. 70304$
$\therefore$ Compound interest =Rs.(70304-62500)=Rs.7804