Question

What is the Present Worth (Pw) of a $80,000 cost in Year 1 which decreases 5% each year up to Year 6? Use i=8%

Answer 1

Solution:

Given, year 1 = 80000

Since it decreases by 5% each year, then future value will be

80000*5% = 4000

So, Year 2 = 80000-4000 = 76000

76000*5% = 3800

So, Year 3 = 76000-3800 = 72200

72200*5% = 3610

So, Year 4 = 72200-3610 = 68590

68590*5% = 3430

So Year 5 = 68590-3430 = 65160

65160*5% = 3258

So, Future value = year 6 = 65160-3258 = 61902

Present worth = F (1/1+i)ⁿ

= 61902*(1/(1+0.08))⁶

= 61902*(1/1.08)⁶

= 61902*(0.925926)⁶

= 61902*0.630169

Present worth = 39008.76