Problem 3. In a certain country it is required that the force of interest for any banking transaction follow the function

4 (St t > 0 50 t’ where t is the time in years since the transaction began.

(1) (5 points) You have deposited $500 in the bank and make no other deposits or withdrawals. How much is this deposit worth at the end of 20 years? (2) (5 points) You have loaned $1,000 for 35 years. You are to repay the loan by making a payment of $400 at time t = 12 and a final payment of X at time t = 35. Compute X.