Question

An N.G.O. wants to invest ₹300000 in a bond which pays \[5\% \] annual interest first year, \[6\% \] interest second year, 7% interest third year and so on. The interest received per year is to be utilized for the education of poor people. If the investment is done for 10 years find the total interest received by N.G.O.

Answer 1

Hint: Calculate the simple interest for each year. Add the interests thus obtained to get the final answer.Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Complete step-by-step answer:
We are given the information about an investment that an N.G.O. wants to make a bond.
Each year the rate of interest increases by \[1\% \].
We are asked to find the total interest received by the N.G.O. if the investment is done for 10 years.
We will use the formula for simple interest to compute the interest received by the N.G.O. in each year.
 $ I = \dfrac{{P \times n \times r}}{{100}} $
Here, I am the principal, n is the period of interest in years, r is the rate of interest per annum.
Given that investment = 300000
Therefore, P = 300000.
Also, n = 1 for each year
For 1st year, r = \[5\% \]
Therefore, interest for 1st year \[ = \dfrac{{300000 \times 1 \times \;5}}{{100}} = 3000 \times 5\]
Similarly, we get
Interest for 2nd year \[ = \dfrac{{300000 \times 1 \times \;6}}{{100}} = 3000 \times 6\]
Interest for 3rd year \[ = \dfrac{{300000 \times 1 \times \;7}}{{100}} = 3000 \times 7\] and so on.
Thus, Interest for 10th year \[ = \dfrac{{300000 \times 1 \times \;14}}{{100}} = 3000 \times 14\]
Therefore, total interest for 10 years \[ = 3000 \times \left( {5 + 6 + 7 + ............ + 13 + 14} \right).....(1)\]
To find \[\left( {5 + 6 + 7 + ............ + 13 + 14} \right)\], we will use the formula of sum of first n terms of an arithmetic progression
\[{S_n} = \dfrac{n}{2}({a_1} + {a_n})\]
Where \[{a_n}\] is the nth term
\[{a_1}\] is the first term
n = number of terms
\[{S_n}\] = sum of n terms.
We have n = 10, \[{a_1} = 5\] and \[{a_n} = 14\]
Therefore,
 \[{S_{10}} = \left( {\dfrac{{10}}{2}} \right)\left( {5 + 14} \right).....(2)\]
On combining (1) and (2), we get
Total interest for 10 years
 \[
   = 3000 \times \left( {5 + 6 + 7 + ............ + 13 + 14} \right) \\
  \begin{array}{*{20}{l}}
  { = 3000 \times \left( {\dfrac{{10}}{2}} \right)\left( {5 + 14} \right)} \\
  { = 3000 \times 95} \\
  { = 285000}
\end{array} \\
 \]
Hence, the total interest received by the N.G.O. is 285000.

Note: Sometimes, in questions related to simple interest, the period of interest is not expressed in years. In such cases, it is imperative to convert the given period in years before using the simple interest formula. For example, if the period is given as 6 months. Then $ n = \dfrac{6}{{12}} = \dfrac{1}{2} $ .