1. A loan is repaid with level installments payable at the end of each half-year for 3(1/2) years, at a nominal rate of interest of 8% convertible semiannually. After the 4th payment, the outstanding loan balance is $5000. Find the amount of the loan.

2. Perpetuities in arithmetic progression. If a perpetuity has first payment P and each payment increases by Q, then its present value, one period before the first payment, is P/i + Q/i^2 . Using this formula, find the present value of a perpetuity-immediate which has annual payments with first payment $360 and each subsequent payment increasing by $40, at annual interest rate 1.3%.

3. Filip buys a perpetuity-immediate with varying annual payments. During the first 5 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase. For year 6 and all future years, the current year's payment is K% larger than the previous year's payment. At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50. Calculate K, given that K < 9.2.