Question

What sum invested for 1½ years compounded half - yearly at the rate of 4% per annum will amount to rupees 132651?​

Answer 1

The principal value or sum is Rs.125000.

Step-by-step explanation:

Given : Sum invested for 1 and 1/2 year compounded half yearly at rate of 4% p.a will amount to Rs.132651.

To find : The sum ?

Solution :

Using compound interest formula,

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

100

r

)

t

Where, A is the amount A=Rs.132651.

P is the principal

r is the rate of interest 4%.

Rate is compounded half yearly so, r=\frac{4}{2}=2\%r=

2

4

=2%

t is the time t=1 and half year = 3 half year

Time is compounded half yearly t=3 years

Substitute values in the formula,

132651=P(1+\frac{2}{100})^3132651=P(1+

100

2

)

3

132651=P(1+0.02)^3132651=P(1+0.02)

3

132651=P(1.02)^3132651=P(1.02)

3

132651=P(1.061208)132651=P(1.061208)

P=\frac{132651}{1.061208}P=

1.061208

132651

P=125000P=125000

Therefore, The principal value or sum is Rs.125000.