Question

Principal (P) =
5.000 ; Time (T) = 3 years; Amount (A)=6500.
Find the interest rate (R) and Simple Interest (SI).​

Answer 1

Answer:

• The rate of interest is 10 % and the simple interest is Rs. 1500.

Given :-

• Principal = Rs. 5000.
• Amount = Rs. 6500.
• Time = 3 years.

To Find :-

• We have to find out the rate of interest and the simple interest.

Formula Used :-

✪ Simple Interest = Amount - Principal ✪

✪ Simple Interest = P × R × T/100 ✪

Calculations :-

~ Here we are given principal, amount and time. We are asked to find out the rate of interest and the simple interest. Then firstly, we will find out the simple interest. And at last, we will find out the rate of interest.

According to the question, we know that :-

✪ Simple Interest = Amount - Principal ✪

~ Where,

• Amount = Rs. 6500.
• Principal = Rs. Rs. 5000.

↦ Simple Interest = Amount - Principal

↦ Simple Interest = Rs. 6500 - Rs. 5000

➦ Simple Interest = Rs. 1500

• Hence, the Simple Interest is Rs. 1500.

~ Now we have the Simple Interest. So now, we will find out the Rate of Interest.

We know that :-

✪ Simple Interest = P × R × T/100 ✪

~ Where,

• Simple Interest = Rs. 1500.
• Principal = Rs. 5000.
• Time = 3 years.

↦ Simple Interest = P × R × T/100

↦ 1500 = 5000 × R × 3/100

↦ 1500 = 50 × R × 3

↦ 1500 = 150R

↦ R = 1500/150

➦ R = 10 %

• Hence, the Rate of Interest is 10 % p.a.

Answer 2

Answer :-

• The simple interest is Rs 1500.
• The interest rate is 10% p.a.

Given :-

• Principal = Rs 5000.
• Time = 3 years.
• Amount = Rs 6500.

To find :-

• The Simple Interest.

Step-by-step explanation :-

• In this question, the principal, time and amount have been given to us. We have to find the interest rate and the simple interest. For this, we are first going to find the simple interest using the principal and amount. Then we will use it to find the interest rate.

----------------

• Before finding the interest rate, we first have to find the simple interest!

We know that :-

$\underline{\boxed {\sf S I = Amount - Principal}}$

Here,

• Amount = Rs 6500.
• Principal = Rs 5000.

$\underline{ \underline{\mathfrak{Substituting \: given \: values \: in \: this \: formula,}}}$

$\boxed{ \bf S I = 6500 - 5000}$

Subtracting 5000 from 6500,

$\overline{ \boxed{ \bf SI = Rs \: 1500}}$

• The simple interest is Rs 1500.

----------------

• Now since we know the simple interest, therefore let's find the interest rate!

We know that :-

$\underline{\boxed{\sf SI = \dfrac{Principal \times Rate \times Time}{100}}}$

Here,

• Simple interest = Rs 1500.
• Principal = Rs 5000.
• Time = 3 years.

• Let the interest rate be r.

$\underline{ \underline{\mathfrak{Substituting \: given \: values \: in \: this \: formula,}}}$

$\rm 1500 = \dfrac{5000 \times r \times 3}{100}$

Multiplying 5000 with 3,

$\rm1500 = \dfrac{15000 \times r}{100}$

Multiplying 15000 with r,

$\rm1500 = \dfrac{15000r}{100}$

Transposing 100 from RHS to LHS, changing it's sign,

$\rm1500 \times 100 = 15000r$

Multiplying 1500 with 100,

$\rm150000 = 15000r$

Transposing 15000 from RHS to LHS, changing it's sign,

$\rm\dfrac{150000}{15000} = r$

Dividing 150000 by 15000,

$\overline{ \boxed{\rm10 = r}}$

• The interest rate is 10% per annum.