Question

the compound interest and simple interest on a certain sum for 2 years is 1230 and 1200 respectively. the rate of interest is same for both and it is compoundede anually .so what is the principle

Answer 1

SOLUTION:-

Simple interest for two years  is 1200 and interest for one year  is 600

So, C.I for 1st year is 600 and for 2nd year is 630.

(Since it is compounded annually, S.I and C.I for 1st year would be same) 

When we compare the C I for 1st year and 2nd year, it is clear that the interest earned in 2nd year is 30 more than the first year. 

Because, interest 600 earned in 1st year earned this 30 in 2nd year. 

It can be considered as simple interest for one year.

That is, principal  =  600, interest  =  30 

I  =  P×r×t / 100

30  =  (600 × r × 1) / 100

30  =  6r

5%  =  r

In the given problem, simple interest earned in two years is 1200. 

I  =  P×r×t / 100

1200  =  (P × 5 × 2) / 100

1200  =  P / 10

Multiply each side by 10.

12000  =  P

So, the principal is 12000