Question

At what rate % p.a. will a sum of Rs. 4000 yield C.I of Rs. 410 in 2 years

Answer 1

Answer:

5%

Step-by-step explanation:

put formula A=P(1+r/100)^t

A=4000+410=4410

t=2

and solve it then we get r=5%

Answer 2

• As per the data given in the question, we have to determine the required number.

          Given data:-  $CI=410Rs.\ in \ 2\ years.$

          To find:-$PA=?$

         Solution:-

          Principal $=4000$

         Compound interest for two years $=Rs.410$

      ∴ Amount at the end of two years $=A=Rs(4000+410)=\text { Rs. } 4410$

       ⇒ Time 2 years

        Let the rate of interest be r% p.a.

         we have,

                 $\Rightarrow \mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{r}}{100}\right)^{2} \\\Rightarrow 4410=4000\left(1+\frac{\mathrm{r}}{100}\right)^{2} \\\Rightarrow \frac{441}{400}=\left(1+\frac{\mathrm{r}}{100}\right)^{2} \\\Rightarrow \frac{21 \times 21}{20 \times 20}=\left(1+\frac{\mathrm{r}}{100}\right)^{2}\\\Rightarrow \sqrt{\frac{21 \times 21}{20 \times 20}}=\frac{\mathrm{r}}{100}+1 \\\Rightarrow \frac{21}{20}-1=\frac{\mathrm{r}}{100} \\\Rightarrow \frac{1}{20}\times100=r\\r=5\%P.A.$

       Hence we will get $P.A=5\%.$