5:Continuous compounding formulas and Euler's number
Let see compounding interest formulas. If P is principal r is interest rate per annum (for 10% interest, r = 0.1) interest for one year = principal *interest rate = P*r . Total amount after one year =Principal + interest =P+Pr. In annually compound interest rate regime P+Pr = P(1+r) become principal at the end of first year. Then the next year interest would be calculated on this principal P(1+r) r would be interest for the second year. At the end of second year, total amount would be = P(1+r)+P(1+r) * r = P(1+r)^2 After n years total amount = P(1+r)^n For the same interest rate r, after 6 months how much interest would have been accumulated? Half of the annual interest , that is Pr/2 If interest is compounded to principal semi-annually, at the end of first 6 months Total amont= P+Pr/2=P(1+r/2). For the next 6 months interest will be calculated on this. Interest =P(1+r/2)* r/2. Total amount at the end...