Tag: introduction to interests

Questions Related to introduction to interests

Oscar earned Rs. $2400$ as simple interest on Rs. `$4500$ for $3$ months. What is the annual rate of interest?

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $16.66\%$

  2. $17.77\%$

  3. $18.88\%$

  4. $19.99\%$

Show answer
Correct Option: B
Explanation:
Given, principal $=4500$, Interest $=$ Rs. $2400$, period $=3$ months
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{2400\times 100}{4500\times 3}$
$\Rightarrow R = 17.77\%$
Therefore, the annual rate of interest is $17.77\%$.

To start a grocery shop, a woman borrowed Rs. $1,500$. If the loan was for four years and the amount of interest was Rs. $150$, what simple interest rate was she charged?

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $1.5\%$

  2. $2.5\%$

  3. $3.5\%$

  4. $4.5\%$

Show answer
Correct Option: B
Explanation:
Given, principal $=$ Rs. $1500$, Interest $=$ Rs. $150$, period $=4$ years
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{150\times 100}{1500\times 4}$
$\Rightarrow R = 2.5\%$
Therefore, the simple interest is $2.5\%$.

Mr. Joshua borrowed Rs. $5000$ for $2$ years to make home improvements. If he repaid a total of Rs. $15,000$, at what interest rate did he borrow the money?

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $15\%$

  2. $25\%$

  3. $35\%$

  4. $45\%$

Show answer
Correct Option: B
Explanation:

Given:
Principal $= 5,000$
Interest $= 15000 - 5000 = 10000$
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{5000\times 100}{10000\times 2}$
$\Rightarrow R = 25\%$

Peter invests $ $5,000$ at $4$% simple annual interest. How much in his investment worth after $2$ months?

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. 5323.66

  2. 5033.33

  3. 5066.33

  4. 5343.67

Show answer
Correct Option: B
Explanation:

If the principal amount is $p$, annual interest is $r$ $\%$ then for simple interest after $n$ years the amount will be $p\left (1+\dfrac {nr}{100}\right)$.
Here $p=5000$, $n=\dfrac {1}{6}$, $r=4$ $\%$
So, the amount after $2$ months is $5000\left (1+\dfrac {2}{300}\right) = 5000\left (\dfrac {151}{150}\right) = 5033.33$

The difference between compound interest and simple interest on an amount of Rs. $15,000$ for $2$ years is Rs. $96$. What is the rate of interest per annum?

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $8$

  2. $10$

  3. $12$

  4. Cannot be determined

  5. None of these

Show answer
Correct Option: A
Explanation:

$\left [15000\times \left (1 + \dfrac {R}{100}\right )^{2} - 15000\right ] - \left (\dfrac {15000\times R\times 2}{100}\right ) = 96$
$\Rightarrow 15000 \left [\left (1 + \dfrac {R}{100}\right )^{2} - 1 - \dfrac {2R}{100}\right ] = 96$
$\Rightarrow 15000 \left [\dfrac {(100 + R)^{2} - 10000 - (200\times R)}{10000}\right ] = 96$
$\Rightarrow R^{2} = \left (\dfrac {96\times 2}{3}\right ) = 64$
$\Rightarrow R = 8$.
$\therefore Rate = 8$%.

Ramesh borrowed $Rs \ 14000$ from a bank on simple interest for a period of $5$ years. He returned $Rs \ 6000$ to the bank at the end of three years and $Rs \ 10,900$ at the end of the five years and closed the account. Find the rate of interest per annum.

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $4 \%$

  2. $4.14 \%$

  3. $6 \%$

  4. $9 \%$

Show answer
Correct Option: B
Explanation:

We have,

$P=Rs.\ 14000$

Ramesh returned $Rs.\ 6000$ to the bank at the end of $3$ years.

And returned $Rs.\ 10, 900$ to the bank at the end of $5$ years.

So, the total amount returned by Ramesh is $6000+10,900=Rs.\ 16, 900$

$T=5\ years$
$R=?$

We know that
$A-P=\dfrac{PRT}{100}$ 

So,

$16900-14000=\dfrac{14000\times R\times 5}{100}$ 

$2900=140\times R\times 5$ 

$R=4.14\%$

Hence, this is the answer.

Find the simple interest rate applied to a principal over $8$ years if the total interest paid equals the borrowed principal.

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $10\%$

  2. $20\%$

  3. $12.5\%$

  4. $15\%$

Show answer
Correct Option: C
Explanation:

We have given that interest and principal are equal.

Let Rs. $x$ be the interest and principal.
Here $T=8$ years
We know $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $x=\dfrac{x\times R\times 8}{100}$
$\Rightarrow$ $R=\dfrac{100}{8}=12.5\%$
Simple interest rate is $12.5\%$.

Find the simple interest rate applied to a principal over $5$ years if the total interest paid equals the borrowed principal.

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $10\%$

  2. $20\%$

  3. $30\%$

  4. $40\%$

Show answer
Correct Option: B
Explanation:

We have given that interest and borrowed principal are same.

Let $x$ be the interest and borrowed principal.
We know $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $x=\dfrac{x\times R\times 5}{100}$
$\therefore$ $R=\dfrac{100}{5}=20\%$

What is the simple interest rate applied to a principal over $2.5$ years if the total interest paid equals the borrowed principal?

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $20\%$ 

  2. $30\%$

  3. $40\%$

  4. $50\%$

Show answer
Correct Option: C
Explanation:

We have given that interest and principal are equal.

Let Rs. $x$ be the interest and principal.
Here $T=2.5$ years
We know $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $x=\dfrac{x\times R\times 2.5}{100}$
$\Rightarrow$ $R=\dfrac{100}{2.5}=40\%$
Therefore, simple interest rate is $40\%$.

Jenn borrowed Rs. $5,000$ for $5$ years and had to pay Rs. $1,500$ simple interest at the end of that time. What rate of interest did she pay?

mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

  1. $5$

  2. $6$

  3. $7$

  4. $8$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  $P=Rs.5000,\,T=5\,years $ and $S.I.=Rs.1500$

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

$\Rightarrow$  $1500=\dfrac{5000\times R\times 5}{100}$

$\Rightarrow$  $R=\dfrac{1500}{250}$

$\therefore$    $R=6\%$