Question

find the principal, if the compound interest compounded half -yearly at the rate of 20% per annum for 18 months is rs 331​

Answer 1

The value of principal is Rs. 1000.

Step-by-step explanation:

Let the principal is  = P

then Amount = principal + compound interest = P + 331

Rate% = 20 % per annum

but the interest is compounded half yearly

so, Rate% (r) = $\dfrac{20}{2}$ = 10 %

and time (t) = 18 months = $\dfrac{3}{2}$  year  =  $\dfrac{3}{2}$ × 2 = 3    (∵compounded half yearly)

Now using the formula of Compound interest

       $A=P[1+\dfrac{r}{100}]^{t}$

∴ P + 331 = $P[1+\dfrac{10}{100}]^{3}$

 P + 331 = $P[\dfrac{11}{10}]^{3}$

 P + 331 = $\dfrac{P\times1331}{1000}$

∴ 331 P = 331000

∴ P  = 1000 Rs.

principal is Rs. 1000.