Question

if the interest is computed half yearly then find the CI on the sum of Rs.18500 at the rate of 40% per annum for 18 months?

Answer 1

Dear Student,
SOLUTION:

Given:
●Interest is computed half yearly.
●Sum is of Rs.18500.
●Rate of 40% per annum.
● Time of 18 Months.

Compound Interest...

$ci = a - p$
Where CI is Compound Interest, A is amount and P is principle....
$a = p(1 + \frac{r}{100} ) ^{n}$
Where a is amount, P is principle, r is rate per annum, and n is time it given years....

In half early the Rate becomes half of the original... (I.e. is the Rate is 10%per annum it will be 5% per annum in half early)

And years are counted as halfs of the years (I.e. If the time is given 1 year then it will be 2 half years in half yearly).

SOLUTION:

$a = 18500(1 + \frac{20}{100} )^{3}$
In Time, we can write 18 months as 1 1/2 years which can be written as 3 half years.

$a = 31968$
So, Compound Interest will be,
$ci = 31968 - 18500$
$ci = 13468$
So, Compound Interest is Rs.13468.

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