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Chapter 7: Comparing Quantities

    Introduction

    Meaning of Percentage

    Converting Fractional Numbers to Percentage

    Converting Decimals to Percentage

    Converting Percentages to Fractions or Decimals

    Use Of Percentages

    Charge Given on Borrowed Money or Simple Interest

    Interest for Multiple Years

    Exercise 7.1

    Exercise 7.2

    What Have We Discussed?

    Extra Curriculum Support

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Chapter 7: Comparing Quantities > Interest for Multiple Years

Interest for Multiple Years

If the amount is borrowed for more than one year the interest is calculated for the period the money is kept for.

For example, if Anita returns the money at the end of two years and the rate of interest is the same then she would have to pay twice the interest i.e.,₹750 for the first year and ₹ 750 for the second.

This way of calculating interest where principal is not changed is known as simple interest.

As the number of years increase the interest also increases.

For ₹ 100 borrowed for 3 years at 18%, the interest to be paid at the end of 3 years is 18 + 18 + 18 = 3 × 18 = ₹ .

We can find the general form for simple interest for more than one year.

We know that on a principal of P at R% rate of interest per year, the interest paid for one year is R×P100. Therefore, interest I paid for T years would be

T×R×P100 = P×R×T100 or PRT100

And amount you have to pay at the end of T years is A = P + I

quantities in the relation I = P×R×T100, you could find the remaining quantity.

1. ₹ 10,000 is invested at 5% interest rate p.a. Find the interest at the end of one year.

Interest = P×R×T100

Substituting the values in the above formula, Solve the Below Questions by using Above formula.

Given that, Principal = , Rate= 5% p.a , T = 1 year

= 10100 = RS

2. ₹ 3,500 is given at 7% p.a. rate of interest. Find the interest which will be received at the end of two years.

Given that, Principal = , Rate= 7% p.a , T = year

= 3500×7×2100 = Rs

3. ₹ 6,050 is borrowed at 6.5% rate of interest p.a.. Find the interest and the amount to be paid at the end of 3 years.

Given that, Principal = 6050 , Rate= 6.5% p.a , T = year

= 6050×6.5×3100 = Rs

4. ₹ 7,000 is borrowed at 3.5% rate of interest p.a. borrowed for 2 years. Find the amount to be paid at the end of the second year.

Given that, Principal = 7,000 , Rate= % p.a , T = year

= 7000×3.5×2100 = Rs

So, the total amount to be paid = Rs 490 + Rs 7000 =Rs 7490.

Example 15: If Manohar pays an interest of ₹ 750 for 2 years on a sum of ₹ 4,500, find the rate of interest.

Instruction

Finding Rate of interest

  • We know that Simple Interest =
  • Using this, we get Rate of interest (R) = %
  • Substituting the values of principal, rate of interest and time
  • We have found the answer.

1. You have ₹ 2,400 in your account and the interest rate is 5%. After how many years would you earn ₹ 240 as interest.

Given that, Principal = , Rate= % p.a , T = ?

Interest = Rs = 2400×7×T100 = = years.

2. On a certain sum the interest paid after 3 years is ` 450 at 5% rate of interest per annum. Find the sum.

Interest = , Rate = 5 , Time = years , Principle = ?

= Interest×100Rate×Time = 450×1005×3 = 4500015 =