# The Doctrine of Interest and Annuities Analytically Investigated and Explained; Together with Several Useful Tables Connected with the Subject

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1808 edition. Excerpt: ...at the interval of 3 years from the payment of the last fine, then the value 24564 (as found by the formula) being multiplied by 1-1576 (= the amount of 1/. at 5 per cent in 3-years) will produce 2 8435 for the number of years purchase, in this case required. The demonstration of this rule will be given in 106. A Table showing the present value of the perpetuity of ll. payable at every interval tlierein mentioned. 105. In the three formulae above given ( 101, 102, 103) I have supposed that p expresses the true rate of annual interest: but they may be easily converted into others which contain the nominal rate only, by referring to what has been said in 61 and 77. Whence it will be found that, by making the substitutions there alluded to, the first formula (in 101) will become-+0-1-= 0 + f)"-i: that the second formula (in 102) will become I--il + tL and that the third formula (in 103) will become., -, / r mv U+f)-1 +-i in' 106. It should be observed also that the three formulae above given, denote the true values immediately after the fine paid at any one renewal; or, on the supposition that the full period of v years will elapse before the payment of the next fine: but at any intermediate time between such renewals, it is evident that the formulae will not express the true value. In such cases we must adopt the correction alluded to, in the note to 10S; the investigation of which; for that particular formula is as follows. Let m denote any period, less than y, between the present time and the payment of the next fine: then will the present value of the first fine be (1-J-f)m; and the present value of the second fine, (1 + f)--TO; and the present value of the third fine, (t +...show more

## Product details

• Paperback | 60 pages
• 189 x 246 x 3mm | 127g
• Miami Fl, United States
• English
• black & white illustrations
• 1236527992
• 9781236527998