If an investment of d dollars is compounded continuously at an annual interest r
ID: 3284348 • Letter: I
Question
If an investment of d dollars is compounded continuously at an annual interest rate r, then the amount of money A(t) earned at time t > 0 (in years) is the solution of the initial value problem where r should be expressed as a fraction rather than as a percentage rate, e.g., an annual interest rate of r = 12% would be expressed as Suppose you have just placed d dollars in a bank account that pays 5 percent (annual) interest, compounded continuously. How much do you have in the account after 4 years? (Do not include dollar signs in your answer.) How long (in years) will it take your money to double? (c) How long (in years) will it take your money to triple?Explanation / Answer
a) d*(e^.05*4)= 1.2214d b)2d= d(e^.05t) ln(2)/.05= t t= 13.86 years. c) 3d= d(e^.05t) ln(3)/.05=t t= 21.97 years. The above calculations have been done using 5% as that is what I feel should be used. However if the answer is revolving around 12, please change 05 to 12.