Calculate the principal which amonts Rs. 9826 after 18 months at the rate of compound interest 2.5% per annum when interest is compunded at the interval of 6 months.

Explanation

Let the principal be Rs.x.
The rate of compound inteest per annum is `2.5%=5/2%`
Time `=18` months `=18/12` years `=3/2` years
Since interest is compounded at the interval of 6 months, the period of time is 2.
`:.` The amount of Rs. `x`in `3/2` years `=Rs.x xx(1+(5/(2xx2))/100)^(3/2xx2)=Rs.x xx(1+1/80)^(3)`
`impliesRs. x xx((80+1)/80)^(3)=Rs.x xx(81/80)^(3)`
As per question `x xx(81/80)^(3)=9826`
`=x xx(81xx81xx81)/(80xx80xx80)=9826`
`impliesx=(9826xx80xx80xx80)/(81xx81xx81)`
`impliesx=9466.54` (approx)
Hence the required principal is Rs. 9466.54 (approx)