Question

anurag invested x amount at rate of 20% on compound interest in scheme and after 2 years he again invest 75%of the initial amount in same scheme if man get 8024 as interest after 3yrs then what will be the initial investment​

Answer 1

Given :

Rate : 20%

Time :Total 3 year. (x amount for 2 years, after 2 years he again invest 75%of the initial amount fir 1 year)

Total interest : 8024 rs

To find :

Initial investment

Solution :

Compound interest is a type of interest taken, in which

the interest gained in one period of time will also be taken as add one value to the principal amount.

The formula for total amount with compound interest :

$\bf \: A = P(1 + \frac{r}{n} )^{nt}$

(equation 1)

where

A = Final amount.

P = Principal amount.

r = Rate ( in decimal)

n = Number of times interest applied per time period.

t = time period

In given case,

Firstly x amount is given as interest for 2 years, at the rate of 20%, it means in decimal its rate is :

$\frac{20}{100} = 0.2$

n = 1, and t = 2

Putting all the values in equation 1,

$\bf \: A = x(1 + \frac{0.2}{1} )^{1 \times 2} \\ \bf \: A = x( {1.2})^{2} \\ \\ \bf \: A = 1.44x$

So

The interest amount for first two years is the difference of final and principal amount, so:

I =A - P = 1.44x - x = 0.44x rs

(equation 2)

It is given that 75 % of initial mmoney (i.e. 0.75 x) will again be invested for third year only.

So in this case,

P = 0.75 x

r = 20 % ( i.e. 0.2)

t = 1 year

n = 1

again putting in equation 1,

Final amount for third year :

$\bf \: A = 0.75x(1 + \frac{0.2}{1} )^{1 \times 1} \\ \bf \: A = 0.75x(1.2) \\ \bf \: A = 0.9x$

So,

in this case,

Interest for third year :

I = A - P = 0.9x - 0.75 x = 0.15 x

(equation 3)

It is given that

Total interest in three years = 8024 rs

So by using equation 2 and 3,

we get

$0.44x + 0.15x = 8024 \\ 0.59x = 8024 \\ x = \frac{8024}{0.59}$

so,

The principal amount in initial case is equal to,

x = 13,600 rs.