Question

Anurag invested Rs. ....... At a Compound annual
interest rate of 20% in a scheme. And after two years
he again invested 75% of the initial amount in the same
scheme. if the person After three years you get rupees
7024 as interest so what will come in the blank.​

Answer 1

Given :

The rate of interest for scheme = $r_1$ = 20%

The time period = $T_1$ = 2 years

The rate of interest for scheme = $r_2$ = 75%

The time period = $T_2$ = 1 year

Total interest after 3 years = I = Rs 7024

To Find :

The principal investment amount = p

Solution :

From Compound interest

Amount = Principal × $(1+\dfrac{rate}{100})^{Time}$

So, Total Amount = p × [ $(1+\dfrac{r_1}{100})^{T_1}$ +  $(1+\dfrac{r_2}{100})^{T_2}$ ]

∵  Interest = Amount - Principal

Or,  Total Interest = Total Amount - Principal

Or,   I =  p × [ $(1+\dfrac{r_1}{100})^{T_1}$ +  $(1+\dfrac{r_2}{100})^{T_2}$ ] - p

Or,  Rs 7024 = p  × [ $(1+\dfrac{20}{100})^{2}$ +  $(1+\dfrac{75}{100})^{1}$ ] - p

Or, Rs 7024 =  p  × [ (1.2)² + 1.75 ] - p

Or, Rs 7024 = 3.19 p - p

Or, 2.19 p = Rs 7024

∴            p = $\dfrac{7024}{2.19}$

i.e Principal Invested = p = Rs 3207

Hence, The principal investment amount is Rs 3207    Answer