Here's my problem : If the compound interest on a sum of money for 3 yr at the rate of 5% per annum is Rs 252.20, the simple interest on the same sum at the same rate and for the same time is ?
Can you please elaborate how to solve this question. I was thinking of an approach that if I do the following: 1) Take the CI given and then divide it by 100*100/105*105, thinking that would give me the CI after 1 year. 2) After I get the CI after an year, I simply would multiply that by 3 and get the SI for 3 years.
Where am I wrong. And if there are any alternate approaches they're welcome. Thanks
If we knew the original debt $A$, then we could easily compute the simple interest. So let us find $A$. For simplicity let $I=252.20$.
Then the total debt after $3$ years (principal plus interest) is $A(1.05)^3$. Thus $$A+I=A(1.05)^3.$$ It follows that $A((1.05)^3-1)=I$, and therefore $$A=\frac{I}{(1.05)^3-1}.$$ Now we know $A$, and can solve the problem. Just multiply $A$ by $(3)(0.05)$.