Engineering Economic Analysis

r Arithmetic Gradient 99 Cash flows of this form may be resolved into two components: A+4G A+2GA+ r 3G 4 r G A+G _.-. -". 3G A A ...

100 MORE INTERESTFORMULAS Multiply Equation 4-15by (1 +i)andfactorout G, or (1 +i)F = G[(1+i)n-l+ 2(1+i)n-2+.". +(n- 2)(1 +i)2+( ...

Arithmetic Gradient 101 A man has purchased a new automobile. He wishes to set aside enough money in a bank account to pay the m ...

102 MORE INTERESTFORMULAS Note that the value ofnin the gradient factor is 5, not 4. In deriving the gradient factor, we had (n- ...

Arithmetic Gradient 103 two components: ,100 t 0~1--'-'---'-2---'---3~4 200 t 400 TI 200 t 300 J A=100 +100(AjG, 6%, 4)= 100+ 10 ...

104 MORE INTERESTFORMULAS gradient. Instead, we willsubtract an increasing gradient from an assumed uniform series of payments. ...

Geometric Gradient 105 150 50 o t 0 -l-- --- -2-3-4 5 6 1! p J 100 r It is important that you closely examine the location ofJ.B ...

106 MORE INTERESTFORMULAS 0-1-2-3-4-5 :.. 1.00 00 -----_ 110.00---_ 121.00-----.... 133.10-....... 146.41' From the table, we ca ...

,. Geometric Gradient 107 : A A 2 __ -A3 -;---r--- f O-1-2-3-..t---n-l-n I p In the general case, wherei=f g,Equation 4-24 may b ...

108 MORE INTERESTFORMULAS The expression in the brackets of Equation 4-29 is the geometric series present worth factor wherei=Jg ...

Nominal and Effective Interest 109 Nominal and Effective Interest Consider the situation of a person depositing $100 into a bank ...

110 MORE INTERESTFORMULAS per year and paid a nominal interest rate per year,r,theinterest rate per compounding subperiodwould b ...

'-,- -_. .. --'.. Nominal and EffectiveInterest 111 If a savings bank pays 11/2%interest every 3 months, what are the nomi ...

-~ ----------------- ------------- 112 MORE INTERESTFORMULAS annually, the nominal interest rate equals the effective interest r ...

Nominal and Effective Interest 113 F =P(1 +i)n=50(1 + 0.20)52 =$655,200 With a nominal interest rate of 1040%per year and effect ...

114 MORE INTEREST FORMULAS 3-month interest period or an effectiveifor each time period between withdrawals. Let's solve the pr ...

----.------ _ d ~ontinuous Gompound~ng^115 ~TjF~~ Compute an effectiveifor the time period between withdrawals. Between withdra ...

116 MORE INTERESTFORMULAS -! - -- ....- r m = Interest rate per interest period mn = Number of compounding subperiods innyears ...

Continu_ous C~mpounding 117 To find compound amount and present worth for continuous compounding and a single payment, we write: ...

118 MORE INTERESTFORMULAS I.... 9V!)- .:~ <-. .~..-~ How long will it take for money to double at 10% nominal interest, compo ...