I Halley (1698) poses the following problem: An annuity of ,20 being in possession for the term of 21 years, and for ,40 paid down it can be prolonged for 10 years more to 31 years; what is the rate of interest required? (Hint: Evaluate the interest rate associated with paying ,40 today for a cash flow of ,20 that will last for 10 years after the 21 year annuity reaches maturity.) ( using Halley formula to calculate )

iiWitt (1613) poses the following problem: A oweth to B ,1200 to be paid in 6 yeares, in 12 equal payments, viz. at the end of each halfe yeare ,100. They agree to cleare this debt in 3 yeares, in 6 equall payments, viz. at the end of each halfe yeare, one payment. The Question is, what each payment ought to be, reckoning interest after the rate of 10 per cent per Ann. and int. upon int.? ( using the Witt formula)