Question

At what rate of compound interest per annum will a sum of rs 20000 become rs 23328 in 2 years

Answer 1

Rate of Interest = 8% p.a.

Step-by-step explanation:

We are given that Rs. 20,000 amounts to Rs. 23,328 in two years compounded annually.

Let the Principal sum of money = P

Rate of Interest = R

Time Period = T

Amount of money = A

As we know that compound interest formula is given by;

         Amount =  $\text{ Principal} \times (1+ \text{Rate of Interest})^{\text{Time}}$

                                      Or

                         $A=P\times (1+R)^{T}$

                       

Now, we are given with P = Rs 20,000 , A = Rs 23,328 and T = 2 years; we have to find the rate of interest ;

So, putting values in above equation we get;

                           $23,328=20,000 \times (1+R)^{2}$

                            $(1+R)^{2} = \frac{23,328}{20,000}$

                             $(1+R)^{2} = 1.1664$

Taking square root on both sides, we get;

                         (1 + R) =  $\sqrt{1.1664}$

                         (1 + R) = 1.08

                           R = 1.08 - 1 = 0.08 or 8%

Therefore, rate of interest is 8% per annum.

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