Question

Find the compound interest on $Rs.1000$ at the rate of $8\%$ per annum for $1\frac{1}{2}$ years when interest is compounded half-yearly?

Answer 1

Principal (P) $=Rs.1000$
Rate (R) $=8\%$ p.a
Period (T) $=1\frac{1}{2}\text{years}=\text{3 half-years}$
$\therefore$ Interest for the first half-year $=\frac{PRT}{100}$
$=\frac{1000\times 8\times 1}{100\times 2}=Rs.40$

Amound after one half-year $=Rs.1040$

or, Principal for the second half-year $=Rs.1040$

Interest for the second half-year

$=\frac{1040\times 8\times 1}{100\times 2}=Rs.\frac{4160}{100}=Rs.41.60$

Amount after second half-year
$=Rs.1040+41.60=Rs.1081.6$

or, Principal for the third half-year $=Rs.1081.60$
Interest for the third half-year
$=\frac{1081.60\times 8\times 1}{100\times 2}=Rs.\frac{4326.40}{100}=Rs.43.264$

$\therefore$ Compound interest for the third half-year
or $1\frac{1}{2}$ years $=Rs.40+Rs.41.60+Rs.43.264=Rs.124.864$

Alternate way:

Interest is compounded half yearly

$\therefore$ Interest @ half year $=\frac{8}{2}=4\%$

n $=$ number of times interest added in $1\frac{1}{2}$ years $=3$

Amount (A) is given by

$A=P[1+\frac{r@halfyear}{100}{]}^n$

$=1000[1+\frac{4}{100}{]}^3$

$=1000\times \frac{104}{100}\times \frac{104}{100}\times \frac{104}{100}$

$=\frac{104\times 104\times 104}{10\times 100}$

$=1124.864$

Compound Interest $=$ Amount $-$ Principal

$=1124.864-1000=Rs.124.864$