Hi,I have been asked this question by a non finance student,which confused me. He said:since the yearly interest has a small value and is compounded daily or weekly, it is reasonable to assume that exponential (rt)-1 approximately equals rt where r is interest and t is time.First of all to my knowledge when interest is continuously compounded as if it means that every second you have interest so I didn't get his point of using continuous compounding and mentioning that the interest is usually compounded daily or weekly.The second point is that is equality correct? exponential (rt)-1 approximately equals rt ?Thanks

Hi, if you are not convinced why not trying numerical examples?

exp(rt)=1+r t+(r^2 t^2)/2+(r^3 t^3)/6+(r^4 t^4)/24+(r^5 t^5)/120+(r^6 t^6)/720+O(r^7) so the right hand terms are small for small r or t

QuoteOriginally posted by: Mballackexponential (rt)-1 approximately equals rt ?exp(rt) = 1 + rt + (rt)^2/2 + ...