Question

find the compound interest on rs 1000 at the rate of 8% per annum for one and a half years when interest is compounded half yearly .

Answer 1

$p(1+\frac{r}{100} ){t}$

$1000(1 + \frac{4}{100} ){3}$
on t we write 3 because in compounded half yearly we have to distribute years so one and half year iss equal to 3 half years
$1000 \times \frac{104}{100} \times \frac{104}{100} \times \frac{104}{100}$

$1000( \frac{1}{1} + \frac{4}{100}) {3}$
$\frac{1124864}{1000}$
$1124.864$
so we subtract the principal value by amount soo
$1124.86 - 1000$
$124.86$
so 124.86 is the answer...

Answer 2

Given:

$Principal (p) = Rs 1000\\Rate (r)=8 \% \\ Time = one and a half years =3 half years = 1.5 years.$

To find:

Compound interest when it is compounded half-yearly.

Solution:

We know that compound interest when interest is compounded half-yearly is:

$A=P\left(1+\frac{\frac{r}{2}}{100}\right)^{2 n}$

Where,

principal = P, rate of interest per unit time = r, number of units of time = n, the amount = A.

On substituting the values we get:

$=1,000\left(1+\frac{8}{200}\right)^{3} \\\\ =1,000(1.04)^{3} \\\\ = 1,124.86 Rs .$

We know that Compound Interest = Amount - principal = 1,124.86 - 1,000 = 124.86 Rs.

Therefore, the compound interest on Rs 1000 at the rate of 8% per annum for one and a half years when interest is compounded half-yearly is 124.86 Rs.