Since the compound interest of $704 is $64 more than the simple interest, the simple interest over two years = 704-64 = 640.sukhman wrote:The difference between compound interest and and simple interest for two years on a certain sum at a certain rate of interest is $64. Find the principal in $ if the compound interest for two years is $ 704
a) 1000 b)1200 c)1600 d)1400 e)1500
Thus, the simple interest for each year = 640/2 = 320.
We can PLUG IN THE ANSWERS, which represent the principal.
When the correct answer choice is plugged in, the compound interest will be $64 more than the simple interest.
Since 320 is equal to 20% of 1600, the correct answer choice is likely to be C, with an annual interest rate of 20%.
C: 1600
Total simple interest over 2 years = (20% of 1600) + (20% of 1600) = 320 + 320.
Compound interest over 2 years:
Interest in the first year = 20% of 1600 = 320.
Interest in the second year = (20% of the principal) + (20% of the first-year interest) = (20% of 1600) + (20% of 320) = 320 + 64.
Total compound interest = 320 + 320 + 64.
(total compound interest) - (total simple interest) = (320+320+64) - (320+320) = 64.
Success!
The correct answer is C.
