By Guy E. Churchill, R Brown, G. Chandler and W. A. Davis (Auth.)
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This type of question can be tackled in several ways, one of which is at our disposal already. It will be noted that the question can not be solved by reference to the tables which are given. 1) to the given figures, 2 3 n ί^+η = 20-7200 = ν + ν + ν + ... + v + t/» 2 3 n = 20-5488 = ν + ν + ν + . . -f v and by subtracting +1 from Ö^+TI, +1 0-1712 = . . ί ^ . 2) 1 — v" a~n\ = —— and substituting η + 1 for n, 1 now substituting the given data, 1 2072 = - 0 1 ι 72 1 = 0 8 28 8 ι Therefore, 20-72 / = 0-8288 ' • = l f = °-04 = 4%.
The given series is: ν + tr + IT ... 1)], Λ aje\ =5-551 + 5-2866 = 10-8376 Therefore ajß\ at 5% = 10-838 to three places. That was an odd annuity in arrears. ) The present value, at an effective rate of interest of 6% per annum, of a special annuity-certain under which payments of 1 are made at the beginning of the first, third, fifth, seventh and ninth years, is 4-014. Find the value of ajöi at an effective rate of interest of 6% per annum.
Ad. = 6d. = %d. = lOd. g. : Is. Ad. = £0-366 667 (Is. = £0-35, plus Ad. = £0-016 667) lis. &d. = £0-583 333 (Us. = £0-55, plus %d. = £0-033 333) 17s. 6d. = £0-875 (17s. = £0-85, plus 6d. —3 46 COMPOUND INTEREST SIMPLIFIED EXAMPLES Write down as decimals of £1 : 45·. ; 165. ; Ss. ; 9s. ; 17s. ; 3s. ; 9s. ; 10s. ; 19s. ; and Is. lOd. CHAPTER 7 Deferred Perpetuities are a combination of the perpetuity referred to in the last chapter, and the deferred annuities referred to in Chapter 5, with the vesting date deferred (in exactly the same way as a deferred annuity's is) for a finite number of years.