Question

Mr. Ramu invested Rs. 9000 at a certain rate of interest compounded annually for three years. If it amounts
160
to Rs. 10,890 at the end of second year, what will be the interest for the third year?​

Answer 1

Step-by-step explanation:

First. Find out the rate and then using rate find the amount of three years and subtract 2 year amount from 3 year amount then we get the interest of third year

Answer 2

According the question,:-

Principal =Rs. 9000                                                   ( given)

Amount after 2nd year =Rs. 10890                         ( given)

Time = 2 years.                                                           ( given)

We have to find out the rate of interest.

Let,s consider rate of interest = r

∴ A = 9000 ( 1 + $\frac{r}{100}$)²

⇒ 10890 = 9000 ( ( 1 + $\frac{r}{100}$)²

⇒$\frac{10890}{9000}$ = ( 1 + $\frac{r}{100}$)²

⇒$\frac{1089}{900}$ =( 1 + $\frac{r}{100}$)²

⇒ ($\frac{33}{30}$)²= ( 1 + $\frac{r}{100}$)²

⇒ $\frac{33}{30}$ = ( 1 + $\frac{r}{100}$)

⇒ $\frac{11}{10}$ =  ( 1 + $\frac{r}{100}$)

⇒ ( $\frac{100 + r }{100}$) = $\frac{11}{10}$

⇒10 ( 100 + r) = 100 ×11

⇒1000 + 10r = 1100

⇒ 10 r = 1100 - 1000= 100

⇒ r = $\frac{100}{10}$ = 10

∴ r = 10%

Now we have to find out the interest for the third year.

Let,s consider the amount after third year will be = A₃

Hence A₃ = 9000 ( 1 + 10% )³  

                 = 9000 ( 1 + $\frac{10}{100}$)³

                 =9000 ( $\frac{110}{100}$)³=    

                 =9000×( $\frac{11}{10}$)³

                 = 9000 × 1.331

                 = 11979

∴the interest for the third year will be :-

                 =( 11979 - 10890)

                 =  1089

Ans :- The interest for the third year will be Rs. 1089.

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