Question

₹6540 amounts to ₹8447.50 at
$12\frac{1}{2} per \: annum$
Find Time​

Answer 1

Time =

Step-by-step explanation:

We have to determine the time period where ₹ 6,540 amounts to ₹ 8447.50 at   $12\frac{1}{2}$ per annum.

Assuming interest is calculated for compound interest.

Let P = Principal sum of money

    R = Rate of interest

    T = Time period

    A = Amount of money

As we know that the formula for calculating amount in case of compound interest is given by;

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

                                            Or

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

                                 

Now, in the question we are provided with P = Rs 6,540 , A = ₹8,447.50 and R =  $12\frac{1}{2}$ % per annum and Time period = T

So,            Amount    =  $6,540\times (1+\frac{25}{2 \times 100} )^{T}$

                ₹8,447.50  =  $6,540\times (1+0.125 )^{T}$

                ₹8,447.50  =  $6,540\times (1.125 )^{T}$

                        $1.125^{T} =\frac{8447.50}{6540}$

                        $1.125^{T} =\frac{31}{24}$

Now, taking log on both sides, we get;

                       $T \times ln(1.125) = ln(\frac{31}{24} )$

                        $T = \frac{ln(\frac{31}{24} )}{ln(1.125)}$    

                        T = 2.2 years

Therefore, the time period is 2.2 years.