During the reigns of King William and Queen Anne, large sums were frequently borrowed upon annuities for
Question:
During the reigns of King William and Queen Anne, large sums were frequently borrowed upon annuities for terms of years, which were sometimes longer and sometimes shorter. In 1693, an act was passed for borrowing one million upon an annuity of fourteen per cent, or of 140,000l. a year for sixteen years. In 1691, an act was passed for borrowing a million upon annuities for lives, upon terms which in the present times would appear very advantageous. But the subscription was not filled up. In the following year the deficiency was made good by borrowing upon annuities for lives at fourteen per cent, or at little more than seven years purchase. In 1695, the persons who had purchased those annuities were allowed to exchange them for others of ninety-six years upon paying into the Exchequer sixty-three pounds in the hundred; that is, the difference between fourteen per cent. for life, and fourteen per cent. for ninety-six years, was sold for sixty-three pounds, or for four and a half years purchase. Such was the supposed instability of government that even these terms procured few purchasers. In the reign of Queen Anne money was upon different occasions borrowed both upon annuities for lives, and upon annuities for terms of thirty-two, of eighty-nine, of ninety-eight, and of ninety-nine years.
i) Assuming arithmetically declining survival rates (uniform death rates), a maximum possible age of86 and a market interest rate of 8%, what is the "breakeven age" for a purchaser of the million , loan life annuity.
ii) Explain how Smith arrives at the solution of 4.5 years purchase for the exchange of the lifeannuity for the term annuity of 96 years at the rate of , 63 of term annuity for ,100 of life annuity
iii) 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.)
Iv) Witt (1613) poses the following problem: A oweth to B ,1200 to be paid in 6 years, in 12 equal payments, viz. at the end of each half year ,100. They agree to clear this debt in 3 years, 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.?
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill