difference between the simple interest and the compound interest?

Question

The difference between the simple interest and the compound interest accrued in two years on a certain sum at a certain rate of interest is Rs 80 . If the simple interest for the second year is Rs 1000 , find the sum .

(1)Rs 10000
(2)Rs 12000
(3)Rs 12500
(4)Rs 15000


what it means ".....If the simple interest for the second year is Rs 1000...."

it says in second year the interest is Rs 1000.
does it means in 2 years 1000+1000 rs = 2000 Rs interest ?

Answer 1

you're right. and the answer is Rs 12500...
if p = principal, i = interest rate,
for simple interest over 2 years = p*i = p*i = 2*p*i
for compound interest = p*i + ( p+p*i)*i = 2*p*i + p*i*i
the difference of these 2 is 80,
hence simplifying gives.... p*i*i = 80
since p*i = 1000, i = 0.08.
therefore, p*0.08 = 1000, p = 12,500

Answer 2

I don't believe you have sufficient info to get a unique answer. For a given sum, there is an interest rate that will meet the criteria of the problem: that the amount returned compounding (one earning period per year for two years) will be1080 Rs extra while at simple interest, (one lump payment in two years), the amount returned will be 1000 Rs extra.