sol9 - MATH MODULE 9 Solutions to Exercises 1 Under...

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1. Under option (a), you would owe Louie 1000(1.02) 364 = $1,350,400.29, whereas under option (b) you would owe him only 1000(1.1) 52 = $142,042.93. The weekly rate is much more of a bargain! 2. We need to solve the equation 300 = 100(1.25) t for t . Simplifying, we have 3 = (1.25) t , and taking the log of both sides and rearranging gives us t = log3/log1.25 = 4.923 years. Hence, Unidyne should reach an annual sales level of $300 million in 2015. 3. In Leutonia, the rate of inflation between 2010 and 2011 was (275 – 250)/250 = 10%/year, whereas in Granfaloonia it was (97 – 88)/88 = 10.227%/year. The infla- tion rate is higher in Granfaloonia. 4. We use the formula V 0 = 100(1 + i ) t , where t is first 5 years and then 10 years. The present discounted values with t = 5 are (a) $100; (b) $78.35; (c) $62.09; (d) $40.19; (e) $13.17; and (f) $3.13. The present discounted values with t =10 are (a) $100; (b) $61.39; (c) $38.55; (d) $16.15; (e) $1.73; and (f) $0.10. 5. With instantaneous compounding, the rate of growth of your real income is simply the rate of growth of your nominal income minus the rate of inflation, or .05 – .03 = 2%/year. Your real income in 2015 will be 100,000 e gt = 100,000 e .
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