Exercise 6.6

1. How long will it take for a sum of ₹12600 invested at 9% per annum become to ₹15624?

Solution:

Given:

Principal = ₹

Rate = %

Let's find the interest first:

Interest = Amount - Principal

= ₹15624 - ₹12600 = ₹

Let's find Time using Simple Interest formula:

Interest=Principal×Rate×Time100

Time=Interest×100Principal×Rate

=×

=

=

= years

= 2 years 8 months

2. At what rate a sum doubles itself in 8 year 4 months?

Solution:

Given:

Let's take Principal = ₹ (any amount)

Time = 8 years 4 months = years

Amount = 2 × Principal (as sum doubles) = 2 × ₹1000 = ₹

Interest = Amount - Principal = ₹2000 - ₹1000 = ₹

Let's find Rate using Simple Interest formula:

Interest=Principal×Rate×Time100

Rate=Interest×100Principal×Time

=×

=

= %

Therefore, sum doubles itself at 12% rate

3. A child friendly bank announces a savings scheme for school children. They will give kiddy banks to children. Children have to keep their savings in it and the bank collects all the money once in a year. To encourage children savings, they give 6% interest if the amount exceeds by ₹10000, and other wise 5%. Find the interest received by a school if they deposit is ₹9000 for one year.

Solution:

Given:

Principal = ₹

Time = year

Since amount is less than ₹10000, Rate = %

Let's calculate interest:

Interest=Principal×Rate×Time100

=××

= ₹

Therefore, the interest received will be ₹450

4. In 4 years, ₹6500 amounts to ₹8840 at a certain rate of interest. In what time will ₹1600 amounts to ₹1816 at the same rate?

Solution:

First, let's find the rate from first case:

Given: Principal (P₁) = ₹

Time (T₁) = years

Amount (A₁) = ₹

Interest = A₁ - P₁ = ₹8840 - ₹6500 = ₹

Let's find Rate:

Rate=Interest×100Principal×Time

=××

= %

Now for second case:

Principal (P₂) = ₹

Amount (A₂) = ₹

Interest = A₂ - P₂ = ₹1816 - ₹1600 = ₹

Let's find Time:

Time=Interest×100Principal×Rate

=××

= years

= 1 year 5 months