A sum of Rs. 1000 is invested at 8 % simple interest per annum. Calculate the interest at the end of 1, 2, 3, .... years. Is the sequence of interests an AP ? Find the interest at the end of 30 years.

Open in App

Solution

Let P be the principle, R rate of interest and I $_{n}$ be the interest at the end of n years.
$I_{n} = \frac{P R n}{100}$
Here,
$P = R s . 1000$ and $R = 8$ % per annum
Therefore,
$I_{n} = R s . (\frac{1000 \times 8 \times n}{100}) = R s . 80 n$
Putting n = 1, 2, 3, ....., we have
$I_{1} = R s . 80, I_{2} = R s . 160, I_{3} = R s . 240$ and so on.
Since $I_{n}$ is a linear expression in n. Therefore, the sequence of interest forms an AP with common difference 80.

Suggest Corrections

Similar questions

Q. A sum of Rs 1000 is invested at 8% per annum simple interest. Calculate the interest at the end of each year. Show that these interest form an AP. Using this fact, find the interest at the end of 30 years.

A sum of Rs 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 making use of this fact.

A sum of Rs 1000 is invested at 8 $%$ simple interest per year. Calculate the interest for first three years and find the sum of the interest for first three years.

Q. A sum of

R s . 1000

is deposited every year at

8

% simple interest. Calculate the interest at the end of each year. Do these interest amounts form an A.P.? If so, find the total interest at the end of

30

years

Q. A sum of ₹ 2000 is invested at 4% simple interest per year. If the total interest at the end of each year forms an AP, then the interest at the end of 30 year will be ____.

Join BYJU'S Learning Program