Answer :
The principal amount is 85227.27 and the interest is 64772.73.
Solution:
Given:
Amount (A)= 150000
Number of years (n)= 8
Rate of interest (r)= [tex]9\frac{1}{2}\%=\frac{19}{2}\%[/tex]
To find: The principal (P)
We know that the principal is the sum of amount and interest. That is, [tex]\bold{P+I=A}[/tex]
This can be written as [tex]\bold{I=A-P \rightarrow(1)}[/tex]
The formula of simple interest is [tex]\bold{I=\frac{Pnr}{100} \rightarrow(2)}[/tex]
On equating (1) and (2) we get,
[tex]\Rightarrow\bold{A-P=\frac{Pnr}{100}}[/tex]
On substituting the values we get,
[tex]\Rightarrow\bold{150000-P=\frac{P\times8\times19}{100\times2}}[/tex]
On solving we get,
[tex]\bold{\Rightarrow 150000-P=0.76P}[/tex]
On grouping the like terms together we get,
[tex]\bold{\Rightarrow 150000=0.76P+P}[/tex]
[tex]\bold{\Rightarrow 150000=1.76P}[/tex]
[tex]\bold{\Rightarrow P=\frac{150000}{1.76}}[/tex]
[tex]\bold{\Rightarrow P=85227.2727\approx85227.27}[/tex]
If principal is 85227.27, then the interest will be [tex]\bold{I=150000-85227.27\rightarrow64772.73}[/tex]