Varying continuous payments are made to amortize a $4000 loan over 15 years at a force of interest of 8%. The payments are such that the outstanding loan balance is a linear function. At time 3.5, a lump sum payment of $500 is made. The regular (varying) payments continue to be made until the loan is fully repaid.
Determine the amount of interest paid in year 8 (between time 7 and 8), and the amount of principal paid in year 8. At what time will the loan be fully repaid?