(Q7).A sum of ₹ 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years.

We know that the formula to calculate simple interest is given by

Simple Interest =
P × R × T
100
So, the interest at the end of the 1styear = ₹
1000 × 8 ×
100
 = ₹
The interest at the end of the 2nd year = ₹
1000 × 8 ×
100
 = ₹
The interest at the end of the 3rd year = ₹
1000 × 8 ×
100
 = ₹

Similarly, we can obtain the interest at the end of the 4th year, 5th year, and so on. So, the interest (in Rs) at the end of the 1st, 2nd, 3rd, . . . years, respectively are , , , . . .

It is an AP as the difference between the consecutive terms in the list is ,

i.e., d = . Also, a =

So, to find the interest at the end of 30 years, we shall find a30

Now, a30 = a + ( – 1) d = + × =

So, the interest at the end of 30 years will be ₹