Question

In how many years will Rs. 7500 amount to Rs. 9000 at 4 % per annum simple interest.​

Answer 1

Time - Simple Interest

Simple Interest is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

But in this question, we have been asked to calculate the time period, which can be calculate only with the formula of simple interest. So, first we we'll use the formula of amount to calculate the simple interest and then we'll use the formula of simple interest to calculate the time Period.

The basic formula of Amount is as follows:

$\boxed{\rm{A = SI + P}}$

The basic formula of Simple Interest is as follows:

$\boxed{\rm{SI = \dfrac{P \times R \times T}{100}}}$

Where,

• A - Amount
• SI - Simple Interest
• P - Principal Amount
• R - Rate of Interest
• T - Time Period

According to the given question, we've been given that,

• Amount, A = Rs. 9000
• Principal amount, P = Rs. 7500
• Rate of interest, R = 4%
• Time period, T = ?

Solution:

First we'll calculate the simple interest using the amount formula and then we can use the simple interest formula to find the time period.

By using the amount formula and substituting all the given values, we get the following results:

$\implies A = SI + P \\ \\ \implies 9000 = SI + 7500 \\ \\ \implies SI = 9000 - 7500 \\ \\ \implies SI = 1500$

Now we got the simple interest value. So we can easily find the time period using the simple interest formula.

By using the simple interest formula and substituting the given values, we get the following results:

$\implies 1500 = \dfrac{7500 \times 4 \times T}{100} \\ \\ \implies 1500 = \dfrac{75\cancel{00} \times 4 \times T}{1\cancel{00}} \\ \\ \implies 1500 = 75 \times 4 \times T \\ \\ \implies 1500 = 300 \times T \\ \\ \implies T = \cancel{\dfrac{1500}{300}} \\ \\ \implies \boxed{\bf{T = 5}}$

Hence, the time period is 5 years.

$\rule{300}{2}$

Important Formulae:

Simple interest SI on a certain sum of money of Rs P invested at the rate of R% per annum for T years is given by,

$\implies \boxed{\rm{SI = \dfrac{P \times R \times T}{100}}}$

Simple interest SI on a certain sum of money of Rs P invested at the rate of R% per month for n months is given by,

$\implies \boxed{\rm{SI = \dfrac{P \times R \times n}{12 \times 100}}}$

Simple interest SI on a certain sum of money of Rs P invested at the rate of R% per day (non-leap year) for d days is given by,

$\implies \boxed{\rm{SI = \dfrac{P \times R \times d}{365 \times 100}}}$

Answer 2

Answer:

5

Step-by-step explanation:

Principle = 7500

Amount = 9000

Rate = 4%

Time = ?