Commercial algebra Volume 2 - Softcover

Inhaltsangabe

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1918 edition. Excerpt: ... It is evident that the payment due at 1 will accumulate interest for 4 yr. if left unpaid until 5. Tts amount will be 1.064 x $800 while the amount of that due at 2 will be 1.063 x $800, and so on. The sum, AB, of these payments is found by adding, thus: A& = (1 + 1.06 + 1.062 + 1.06s + 1.064) x $300. It is evident that the quantity in parentheses is the amount of an annuity of 1 per annum for 5 yr. at 6%, or that As = Rsj. In general, A n = Hence we need to find an expression for.s at the rate i. 125. Final Value of 1 per Annum. Let an ordinary annuity of 1 per annum be payable for n years, and let the rate of interest be i per annum. As in § 124, we have Amount of first payment =(l + t)-1. Amount of second payment = (l + i)'1-2. Amount of nth payment =1. Adding, = 1 + (1 + i) +... + (1 + 2 + (1 +?")"-1. In this geometric series, a = 1, r--1 + i, n = n. Since the sum of a geometric series is--, we have (i + Qp-i (i + iy-1 i 1 (i + /)-i / fi + 'J l A table of values of s-j will be found on page 218. 126. Final Value of R per Annum. It is evident that if the annual rent is R per annum, instead of 1, the amount in n years ia lt(l+iy-1 + R0.+iy-2-+ R(l + i) + R, or-R(l+0"-1 + (l + 0"-2H h(l+t')+l, which is equal to RS. If we designate the amount of R per annum for n years by An, we have = =f(i+0"-i1. 127. Illustrative Examples. 1. A trustee deposited $200 in a savings bank at the end of each year for 7 yr., the bank paying 4% per annum, accumulated annually. Find the amount to his credit after he makes the seventh deposit. Since R = $200, i = 0.04, n =7, we have A, = (1.047-1), or $200 xsT1at4%. 0-04 Using the table, page 220, A1 = 7.8982945 x $200 = $1579.66. If a table of final values of 1 were not...

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