How much should you put away into an account that bears an average interest

How much should you put away into an account that

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How much should you put away into an account that bears an average interest rate of 7% pa in order to cover the costs of education? Assume that your child will start college at age 18, your first investment occurs at year 1, and that payments are made at the end of years 18, 19, 20, and 21. Also assume that you continue to invest until he/she graduates.
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Copyright - R.Turton and J. Shaeiwitz 2008 More Examples on Cash Flow Calculations 0 1 2 3 18 19 20 21 $ 18,000 A 21 4 4 21 ,0.07,21 18,000 ,0.07,4 (1 0.07) 1 (1 0.07) 1 (18,000) 0.07 0.07 (1 0.07) 1 (18,000) $1,781.31 (1 0.07) 1 F F A A A A A = + + = + = = +
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Copyright - R.Turton and J. Shaeiwitz 2008 More Examples on Cash Flow Calculations How much would you need to invest in a lump sum at the time of the birth of your child to pay for the education? What are the balances in the investment account in years 18, 19, 20, and 21 just before the $18,000 withdrawals have been made?
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Copyright - R.Turton and J. Shaeiwitz 2008 More Examples on Cash Flow Calculations 0 1 2 3 18 19 20 21 $ 18,000 P ( ) ( ) ( ) ( ) 48 . 301 , 19 $ 07 . 1 07 . 0 1 07 . 1 000 , 18 07 . 0 1 07 . 0 1 000 , 18 07 . 0 1 4 , 07 . 0 , 000 , 18 21 , 07 . 0 , 21 4 4 21 = = + = + = P P A F P F P
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Copyright - R.Turton and J. Shaeiwitz 2008 More Examples on Cash Flow Calculations 0 1 2 3 18 19 20 21 $ 18,000 18 18 19 20 21 ,0.07,18 (19,301.48)(1 0.07) $65,237.70 (65,237.70 18,000)(1.07) $50,544.33 (50,544.33 18,000)(1.07) $34,822.44 (34,822.44 18,000)(1.07) $18,000.00 F F P P F F F = = + = = = = = = = P F 18 F 19 F 20 F 21
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9.6 INFLATION As a result of inflation, a ringgit set aside (not invested) will purchase fewer goods and services in the future than the same ringgit would today. Inflation of costs of equipment, labour, and fuel could be tracked by CEPCI. Sometimes it is desirable to express these trends of costs in terms of inflation (f). CEPCI (j+n) = CEPCI (j) (1 + 𝑓𝑓 ) 𝑛𝑛 eqn 9.15 where n = time span in years f = average inflation rate over the time span j = arbitrary year
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Example 9.18 What was the average rate of inflation for the costs associated with building a chemical plant over the following periods? (a) 1995 through 2001 (b) 2001 through 2007 From Table 7.4 (pg 167), the values of CEPCI are: CEPCI (1995) = 381 CEPCI (2001) = 394 CEPCI (2007) = 500 Eqn (9.15) gives (a) CEPCI (2001) = CEPCI (1995) (1 + 𝑓𝑓 ) 6 394 = 381 (1 + 𝑓𝑓 ) 6 f = 0.006 or 6% per annum
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(b) CEPCI (2007) = CEPCI (2001) (1 + 𝑓𝑓 ) 6 500 = 394 (1 + 𝑓𝑓 ) 6 f = 0.049 or 4.9% per annum.
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To understand inflation, it is necessary to distinguish between cash and purchasing power of cash (for the purchase of goods and services). Inflation decreases this purchasing power with time. All the previous discussions on A, P, and F are given in terms of cash and not in terms of the relative purchasing power of this cash. The term 𝐹𝐹 is introduced, which represents the purchasing power of future cash. This purchasing power can be estimated using eqn (9.16): 𝐹𝐹 = 𝐹𝐹 ( 1+𝑓𝑓 ) 𝑛𝑛 eqn 9.16 Now, from basic eqn 𝐹𝐹 𝑛𝑛 = P (1 + 𝑖𝑖 ) 𝑛𝑛 eqn 9.5 We substitute F in eqn 9.16 in terms of P from eqn 9.5, to get: 𝐹𝐹 = P ( 1+𝑖𝑖 ) 𝑛𝑛 ( 1+𝑓𝑓 ) 𝑛𝑛 = P 1+𝑖𝑖 1+𝑓𝑓 𝑛𝑛 eqn 9.17
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Eqn (9.17) is now written in terms of an effective interest rate
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