This a question from an "Interest Theory" course:

1. (10 points) Am investor makes deposits in the following two accounts: Account 1: Two deposits: 500 at time 2 years from now and 1000 at time 5 years from now, assuming a force of interest 8t ,t> 0, and t is measured in years. 0.4 1+0.2t Account 2: Two deposits: 90 at time n years from now, and 180 at time 5n years from now, where n is a positive real number. It is assumed an effective annual discount rate of 2%. If the accumulated value at time 16 years from now in account 1 is equal to the accumulated value at time 9n years from now in account 2, calculate n. 1. (10 points) Am investor makes deposits in the following two accounts: Account 1: Two deposits: 500 at time 2 years from now and 1000 at time 5 years from now, assuming a force of interest 8t ,t> 0, and t is measured in years. 0.4 1+0.2t Account 2: Two deposits: 90 at time n years from now, and 180 at time 5n years from now, where n is a positive real number. It is assumed an effective annual discount rate of 2%. If the accumulated value at time 16 years from now in account 1 is equal to the accumulated value at time 9n years from now in account 2, calculate n