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 to that 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