a certain sum amount to $ 1400 in 2 yrs and $ 2000 in 5 years on certain fixed simple interest . in how many yrs would the amount be $ 1640 had it been put at the rate of interest compounded annually ?
Choices.
A) 4.5 B) 3.5 C) 3 D) 2 E) 1.5

Rationale: we can form equations as following : initial amount = p , total amount after interest = t , interest per year = i t = p + i given t 1 = p + 2 i = 1400 t 2 = p + 5 i = 2000 from this we get , p = 1000 i = 200 $ now we know that simple interest is < compound interest ( ci = si only after 1 st year if ci is compounded annually ) consider simple interest - after 1 st yer it is 200 $ , after 2 nd years it is 400 $ and after 3 rd year it is 600 $ . to get a 240 $ compound interest the duration have to be > 1 year and < 2 years . only option fitting : option e .
Answer: E