Here's a question on compound interest and simple interest.
The difference in compound interest and simple interest for 2 years on a sum of money is \$160. If the simple interest for 2 years be \$2,880, the rate percent is ____ ?
How do I do it?
[Math] Subtract simple interest from compound interest
finance
Best Answer
Let's call the original principal $P$, and the interest rate $r$. Then the interest accrued in the first year is $Pr$.
If the interest is simple, the interest accrued in the second year is the same, $Pr$ again, for a total of $2Pr$. But if the interest is compound, the interest in the second year is on the original principal plus the first year's interest, $P + Pr$, and so is $(P + Pr)r = Pr + Pr^2$, rather than just $Pr$. The difference between the simple and compound interest accrued in two years is therefore $Pr^2$.
We are given that the simple interest is $2Pr = \$2,880$, and the difference between the two kinds of interest is $Pr^2 = \$160$. Dividing the second by the first gives:
$${ Pr^2\over 2Pr} = {160\over 2880} \\ \frac r2 = \frac1{18}\\ r = \frac19 $$
Or if you prefer, 11.1%.
Then we can solve for the original principal $P$, and then check the values for $P$ and $r$ by calculating the simple and compound interest amounts on $P$ at rate $r$ to see if they match the givens in the question,