Question

A principal that will amout to 150000 for 8 years at 9/1/2 %​

Answer 1

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)= $9\frac{1}{2}\%=\frac{19}{2}\%$

To find: The principal (P)

We know that the principal is the sum of amount and interest. That is, $\bold{P+I=A}$

This can be written as $\bold{I=A-P \rightarrow(1)}$

The formula of simple interest is $\bold{I=\frac{Pnr}{100} \rightarrow(2)}$

On equating (1) and (2) we get,

$\Rightarrow\bold{A-P=\frac{Pnr}{100}}$

On substituting the values we get,

$\Rightarrow\bold{150000-P=\frac{P\times8\times19}{100\times2}}$

On solving we get,

$\bold{\Rightarrow 150000-P=0.76P}$

On grouping the like terms together we get,

$\bold{\Rightarrow 150000=0.76P+P}$

$\bold{\Rightarrow 150000=1.76P}$

$\bold{\Rightarrow P=\frac{150000}{1.76}}$

$\bold{\Rightarrow P=85227.2727\approx85227.27}$

If principal is 85227.27, then the interest will be $\bold{I=150000-85227.27\rightarrow64772.73}$