Problem 4-95(algorithmic) Question Help A cash flow senes is increasing geometri

Question

Problem 4-95(algorithmic) Question Help A cash flow senes is increasing geometrically at the rate of 9% per year. The initial payment at EOY 1 is $5 with ncreasing amal payments endng a years and 5% compounded annually for the remaining 14 years. Find the present amount that is equ valent to this cash flow. 2 The rterest rate is 1 % compounded anua y for the first six Click the icon to view the interest and annuity table for discrete compounding when the MARR is 5% per year. Click the icon to view the interest and annuity table for discrete compounding when the MARR % per year Click the icon to view the interest and annuity table for discrete compounding when the MARR is 13% per year The present amount that is equivalent to this cash flow serieX Sorry, that's not correct One way to find the present amount of the cash flow series is to calculate the present amount of the cash flows when the higher interest rate is applied and the present amount of the cash flows when the lower interest rate is applied. Then find the sum of the obtained values. Recall the formula for the present equivalent for the geometric gradient series: iti -i

Explanation / Answer

Present value of EOY1-6=5500/1.13+5500*1.09/1.13^2....5500*1.09^5/1.13^6=5500/1.13*(1-(1.09/1.13)^6)/(1-1.09/1.13)=5500*(1-(1.09/1.13)^6)/(1.13-1.09)=26737.93986
Present Value of EOY7-20=1.09^6/1.13^6*(5500/1.05+5500*1.09/1.05^2...5500*1.09^13/1.05^14)=(1.09/1.13)^6*(5500/1.05*(1-(1.09/1.05)^14)/(1-1.09/1.05))=(1.09/1.13)^6*(5500*(1-(1.09/1.05)^14)/(1.05-1.09))=76182.05958

Total Present Value=26737.93986+76182.05958=$102919.99944

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