Rohit invests Rs 15625 for three years at a certain rate of interest, compounded annually. At the end of one year, it amounts to Rs 16875. Calculate: (i) the rate of interest per annum. (Ii) the interest accrued in the second year. (iii) the amount due to him at the end of third year. (iv) the interest earned in the third year. (v) the compound interest earned in 3 years.

Answer :

Here the principal amount; P = Rs.15625
Time; t = 1 year
i) Suppose the rate of interest be r % per annum.
So amount accumulated at the end of 1 year is given by;

A = P${\left[1 + \frac{r}{100}\right]}^t$ = Rs.16875

⇒ 15625 ​${\left[1 + \frac{r}{100}\right]}^1$ = 16875

⇒ 15625 + 15625 ​$\frac{r}{100}$ = 16875

⇒15625$\frac{r}{100}$  = 1250

​⇒r  = $\frac{1250 \times 100}{15625}$ = 8% 

Therefore rate of interest is 8% per annum.                            ( Ans )

ii) Also the amount accumulated at the end of the second year (taking t = 1 years) is given by;
As P = 16875​ , r  = 8% 

A₂ = P${\left[1 + \frac{r}{100}\right]}^t$ ​

= 15625 ​ ${\left[1 + \frac{8}{100}\right]}^2$

= 15625 × ${\left(\frac{27}{25}\right)}^2$

= 15625 × $\frac{27}{25}$ × $\frac{27}{25}$= 18225  
So
Interest earned in second year = total ammount after two year - Tataol amount after 1 year

Therefore interest earned in the second year = Rs.18225 - Rs.16875​= Rs.1350   ( Ans )

iii) Now the amount accumulated at the end of third year (taking T = 3 years) is given by;

A₃ = P${\left[1 + \frac{r}{100}\right]}^t$

= 15625  ${\left[1 + \frac{8}{100}\right]}^3$

= 15625×${\left(\frac{27}{25}\right)}^3$

= 15625×$\frac{27}{25}$×$\frac{27}{25}$× $\frac{27}{25}$ = 19683 

Therefore amount accumulated at the end of third year is Rs.19683  

iv )​ Interest earned in thrid year = Tital ammount after 3 year - Total amount after 2 year

Interest earned in third year  =  Rs.19683    - Rs.18225   = Rs . 1458

v ) Compound interest earned in 3 years  = total ammount after three years  -  starting money 

= ​ Rs.19683    - Rs.15625 ​   = Rs . 4008