Question

a certain sum of money, the difference between the compound interest for a year, payable half yearly and the simple interest for a year is rs.180. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.

Answer 1

Answer:

Step-by-step explanation:For ,

N=1year

R=10 %  

We have S.I.=  

100

PNR

​  

=  

100

P×1×10

​  

=Rs0.1P

When interest being compounded for half yearly, for  1  year

We have, N=2  

And R=  

2

10

​  

=5 %  

AndAmount=P(1+  

100

R

​  

)  

N

=P×(1+  

100

5

​  

)  

2

=P×1.05  

2

=1.1025P

And C.I.=A−P=1.1025P−P=0.1025P

Given, C.I.−S.I.=Rs180

⇒0.1025P−0.1P=Rs180

⇒0.0025P−Rs180

⇒P=Rs72,000