Question

What sum invested for 2 years at 12% compounded annually will glow to Rs.4390.40?
(a) Rs.4000
(b) Rs.3500
(c) Rs.3800
(d) Rs.3875

Answer 1

3500 is the correct answer..

Amount= 4390.40
Rate=12%
Time=2 years
Principal=?

Let the principal be P

A= P(1+12/100)*2
A= P(112/100×112/100)
A= P(28/25×28/25)
A= P(784/625)
4390.40= P(784/625)
(4390.40×625)/784=P
3500=Principal

Hope it helps..

Answer 2

Given:

A sum invested for 2 years at 12% compounded annually will glow to Rs.4390.40.

To find:

The sum.

Solution:

As we know that the if a sum 'P' is invested for time 't' years at the rate of 'R%' compounded annually then its amount after 't' years is given by:

$A = P({1 + \frac{r}{100}) }^{ t}$

Now,

As given, we have,

Rate of annual compound interest = 12%

Time = 2 years

The amount obtained after 2 years = Rs.4390.40

So,

The principal 'P' or sum is obtained by

$4390.40 = P {(1 + \frac{12}{100} )}^{2}$

$4390.40 = P {(1 + \frac{3}{25} )}^{2}$

On taking 25 as LCM, we get

$4390.40 = P {( \frac{28}{25} )}^{2}$

$4390.40 = P {( \frac{28}{25}\times \frac{28}{25})}$

On solving, we have,

$\frac{4390.40 \times 25\times 25}{28 \times 28} = P$

${5.6 \times 25\times 25} = P$

${3500 Rs.} = P$

Hence, the correct option is (b) Rs.3500.