By A. H. Pollard (Auth.)
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Additional resources for An Introduction to the Mathematics of Finance, Edition: Revised
A. and the new equation of value . . B. T h e "capital gain" is here a loss of $4 on maturity which is an allowable deduction for tax purposes. e. a. a. a. a. a. '. V. 93 8-3 T h i s could also be obtained by interpolation, b u t it is simpler to use the result of Exercise 8-2. 75. V.
04)- + X ( 1 . 0 4 ) - = 700 ( 1 . 0 4 ) 700 ( 1 . 04) - 14 = $57 to the nearest $1 It would have been equally possible to equate the two sets of payments at the end of 14 years, giving 12 2 200 ( 1 . 0 4 ) + 3 0 0 ( 1 . 0 4 ) 6 + X = 700 ( 1 . 04) = $57 as before. T h e calculation has thus been considerably simplified, a n d it is well worth spending a little time selecting the best p o i n t of time to equate the payments. TIME OF ONE PAYMENT UNKNOWN Problem 2: W h e n should $3000 be paid to be equivalent at 4 % interest to $1000 due in five years' time a n d $2000 due in 10 years?
44 COMPOUNDING MORE FREQUENTLY T H A N A N N U A L L Y Problem 3: Find to the nearest $ the a m o u n t of an a n n u a l a n n u i t y of $200 after 12 years, first payment in one year's time, at a nominal rate of 6 % convertible quarterly. 06136 = $3,402 By interpolation, using S~^\ tables at 6 % and 6 £ % we obtain $3401. B. ) Often, in practice, annuities are payable more frequently than annually—say, monthly, half yearly, etc. Usually in such cases interest is added with the same frequency.