If we want to invest 3000 into an account for 40 months and

If we want to invest $3000 into an account for 40 months, and we have the following two choice: (a). annual rate 8% and compounded monthly. (b). annual rate 7%and compounded continuously. Then what\'s the account value of after 40 month for each of the cases above and which one is the better choice? Account value of (a) after 40 month: _____ Account value of (b) after 40 month: _____ Which one is better? (Circle one) Account (a) or Account (b) (a) Given the arithmetic sequence 3, -1, -5, -9.... find the 30^th term the sum of the first 30 terms. 30^th term = _____ Sum = ______

Solution

Dear Student Thank you for using Chegg !! Given Principle (P) = 3000 $ Time (T) = 40 Months = 40/12 years Option a) Interest Rate (\'r) = 8 % Compounded monthly means n = 12 Formulae used Amount = P (1 + r/100n)^nT (Where T is no of years) = 3000(1+8/(100*12))^40 = 3913.350833 $ Option b) Interest Rate (\'r) = 7% Compounded Continuously Formulae used Amount = Pe^rt (Where t is time in years) = 3000*e^(7/100)*(40/12) = 3788.40703 $ Clearly since amount is more incase of Option a). Hence Option a is better.