Question

Suppose that you have a series of payments: $100 in year 1, $150 in year 2 and $200 in year 3. If annual interest rate is 10%, what is the equivalent uniform series for this gradient series?

Answer 1

Answer:

equivalent annual series = 146.82

Explanation:

given data

payments year 1 = $100

payments year 2 = $150

payments year 3 = $200

annual interest rate = 10%

time = 3 year

solution

we get here equivalent annual series that is express as

equivalent annual series = annual interest rate × net present value ÷ ( 1 -$(1+r)^{-t}$ )    .................1

here net present value = $\frac{100}{(1+0.10)} +\frac{150}{(1+0.10)^2} +\frac{200}{(1+0.10)^3}$  

net present value = 365.14

so her from equation 1

equivalent annual series = 0.1 × $\frac{365.14}{1-(1+0.10)^{-3}}$

equivalent annual series = 146.82