Suppose your uncle takes the 40000 now and wishes to invest

Suppose your uncle takes the $40,000 now and wishes to invest it. He calls you because he is confused from an ad he sees. Investments-R-Us is offering the Euler Fund which compounds continuously and the Daley Fund which compounds 360 days per year. “They are both the same, aren’t they?” he asks. You smile. If each account boasts a nominal annual return of 5%, how much more is in the Euler Fund after 10 years of compounding?

Solution

Compounding per day Frequency n 360 Initial Amount A 40000 Term(years) T 10 Rate r 5% FinalAmount A*(1+r/n)^nT 65946.56 Compounding Continous Frequency n infinity Initial Amount A 40000 Term(years) T 10 Rate r 5% FinalAmount A*exp(r*T) 65948.85 Euler Fund after 10 years of compounding is more by $         2.29