Question

plz help to solve thi problems 20. & 21. ...​

Answer 1

Q 20. Rate of Interest = 8% p.a.

Q 21. Time period = 2 years

Step-by-step explanation:

Let Principal sum of money be represented as = P

     Rate of interest per annum = R%

     Time period = T years

     Amount of money = A

Now, as we know that Amount of money after T years formula is given by;

                $Amount = Principal \times (1+R.O.I.)^{Time}$

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

Q 21 : In this question we are given with A = Rs 69984, P = Rs 60000, Time Period = 2 years

And we have to find the rate of interest per annum;

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

Putting the given values in the above equation we get;

                  69984 = $60000 \times (1 + R)^{2}$

                   $(1+R)^{2} = \frac{69984}{60000}$

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

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

                     1 + R = 1.08

                      R = 1.08 - 1 = 0.08 or 8%

Therefore, rate of interest of 8% p.a. will amount Rs 60000 to Rs 69984 after period of 2 years.

Q 22 : In this question we are given with A = Rs 46656, P = Rs 40000, Rate of Interest = 8% p.a.

And we have to find the Time period ;

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

Putting the given values in the above equation we get;

                  46656 = $40000 \times (1 + \frac{8}{100} )^{T}$

                   $(1+0.08)^{T} = \frac{46656}{40000}$

                    $(1.08)^{T} = 1.1664$

Now taking log on both sides we get;

                    $ln((1.08)^{T}) = ln(1.1664)$

                     $T \times ln(1.08) = ln(1.1664)$

                            $T = \frac{ln(1.1664)}{ln(1.08)}$

                            T = 2 years

Therefore, time period in which Rs 40000 will amount to Rs 46656 at 8% p.a. rate of interest is 2 years.