Question

Suppose Rakesh has invested Rs. 20,000 at 12% simple interest per year. With the return from the investment, he wants to buy a colour. T.V. that cost Rs. 25,000. For what ** should he invest Rs. 20,000 so that he has enough money to buy a colour T.V.?

Answer 1

Step 1. Formulation of the problem :

Here, we know the principal and the rte of interest in the amount Rakesh needs in addition to Rs. 20,000 to buy the colour T.V. We have to find the number of years.

Mathematical Description :

The formula for simple interest is

*.I = Pnr/100

Where P = Principal

n = Number of years

r% = Rate of interest

*.I. = Interest earned

Here, the principal = Rs. 20,000

The money required by Rakesh for buying a colour T.V. = Rs. 25000

So, the interest to be earned = Rs. (25,000 - 20,000) = Rs. 5,000

The number of years for which Rs. 20,000 is deposited = n

The Interest of Rs. 20,000 for n years at the rate of 12% = *.I.

Give the relationship between the number of years and interest, if Rs. 20,000 is invested an annual interest rate of 12%. We have to find the ** in which the interest earned is Rs. 5,000. Putting *.I. = 5,000 in (1),

we have

5,000 = 2400n

Step 2. Solution of the problem :

Solving equations (2), we get

n = 5000/2400 = 50/24 = 2(1/12)

Step 3 : Interpretation : Since n = 2(1/12) and one twelfth of a year is one month Rakesh can buy a colour T.V. after 2 years and one month.

Step 4. : Validation of result

We have to assume that the interest rate ** the same for the ***** for which we calculate the interest.

Otherwise, the formula *.I. = pnr/100 will into be valid. We have also assumed that the price of the colour T.V. machine does not increase by the time 2(1/2) year.