Explanation Formula used: Table Period = No . of years * No . of times the Interest is compounded per year ... ( 1 ) Rate used = Annual Interest rate No . of times the Interest is compounded per year ... ( 2 ) Present value = Present value factor * future value ... ( 3 ) Interest Earned = Future value − Present value ... ( 4 ) Calculation: (a) Note that the interest is compounded annually. Hence, No . of times the interest is compounded per year = 1 . Substitute, No . of times the interest is compounded per year = 1 , No . of years = 6 in equation (1) as follows. No . of periods = No . of years * No . of times the Interest is compounded per year = 6 * 1 = 6 Hence, number of periods is 6. Substitute, Annual Interest rate = 8 % , No . of times the interest is compounded per year = 1 in equation (2) Rate of each period = Annual Interest rate No . of times the Interest is compounded per year = 8 1 = 8 Thus, the rate used is 8%. Calculate the Present Value Factor as follows. Note that, Rate used = 8 % , No . of periods = 6 . From Table 12.3, note that the present value factor is $ 0.6302 . Substitute, Present value factor = $ 0.6302 , Future value = $ 2 , 500 in equation (3). Present value = Present value factor * future value = 0 .6302 * 2,500 = 1,575 .50 Hence, present value is $1,575.50. Substitute, Present value = $ 1 , 575.50 , Future value = $ 2 , 500 in equation (4). Interest Earned = Future value − Present value = 2,500 − 1,575 .50 = 924 .50 Hence the interest Earned is $924.50. (b) Note that the Interest is compounded semiannually. Hence, No . of times the interest is compounded per year = 2 . Substitute, No . of times the interest is compounded per year = 2 , No . of years = 10 in equation (1) No . of periods = No . of years*No . of times the Interest is compounded per year = 10*2 = 20 Hence, Number of periods is 20. Substitute, Annual Interest rate = 6 % , No . of times the interest is compounded per year = 3 in equation (2) Rate of each period = Annual Interest rate No . of times the Interest is compounded per year = 6 2 = 3 Thus, the rate used is 3%. Note that, Rate used = 3 % , No . of periods = 20 . From Table 12.3 note that the present value is 0.5537. Substitute, Present value factor = 0.5537 , Future value = $ 4 , 600 in equation (3). Present value = Present value factor * future value = 0 .5537 * 4,600 = 2,547 .02 Hence, present value is $2,47.02. Substitute, Present value = $ 2 , 547.02 , Future value = $ 4 , 600 in equation (4). Interest Earned = Future value-Present value = 4,600-2,547 .02 = 2,052 .98 Hence Interest Earned is $2,052.98. (c) Note that the interest is compounded semiannually. Hence, No . of times the interest is compounded per year = 2 . Substitute, No . of times the interest is compounded per year = 2 , No . of years = 8 in equation (1) No . of periods = No . of years * No

12th Edition

ISBN: 9781259540554

Author: Jeffrey Slater, Sharon Wittry

Publisher: McGraw-Hill Education

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Chapter 12.2, Problem 3AH

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The Present value and Interest earned of each of the following.

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