Question

At what rate percent per annum will a sum of R s. 31250 amount to Rs. 35152 at Compound Interest in 1 1/2 years interest being compounded half yearly?

Answer 1

At 8% per annum will a sum of Rs 31250 amount to Rs 35152 at Compound Interest in 1 1/2 years.

Step-by-step explanation:

We are given that a sum of Rs 31250 amount to Rs 35152 at Compound Interest in 1 1/2 years where interest being compounded half-yearly.

Let the Principal sum of money be 'P'

Rate of interest per annum be 'R'

Time period be 'T'

and the amount of money be 'A'.

The formula for calculating amount when interest is compounded half-yearly is given by;

                  $\text{Amount}= \text{Principal} \times (1 + \frac{\text{Rate of interest}}{2})^{(\text{Time} \times 2)}$

                                             Or

                              $\text{A}= \text{P} \times (1 + \frac{\text{R}}{2})^{(\text{T} \times 2)}$

Here, P = Rs 31250, A = Rs 35152 and T = $1\frac{1}{2} =\frac{3}{2}$ years.

Now, putting these value in the above equation to calculate R;

   $\text{A}= \text{P} \times (1 + \frac{\text{R}}{2})^{(\text{T} \times 2)}$

   $35152= 31250 \times (1 + \frac{\text{R}}{2})^{(\frac{3}{2} \times 2)}$

   $\frac{35152}{31250} = (1 + \frac{\text{R}}{2})^{3}$    

   $1.125= (1 + \frac{\text{R}}{2})^{3}$

   $( 1.125)^{\frac{1}{3} } = (1 + \frac{\text{R}}{2})$

   $1.04 = (1 + \frac{\text{R}}{2})$

    $\text{R}= 2 \times (1.04 - 1)$

    R = 0.08 or 8%

SO, the rate of interest per annum is 8%.