Question

A settlement in a court case awards an individual year end payments for 20
years, with the first coming one year from now. These will be deposited into an
account earning 3% annual effective interest. The first payment is $4000 and
each payment after that is 2% greater than the previous payment. The recipient
of this settlement has the option of accepting the present value of this payment stream as a single lump sum payment. What is this lump sum amount?

Answer 1

Present value of Annuity with growth formula for period end payments is as followed :

Where,

A = first payment = $4000

i   = 3% p.a.

g = 2% p.a.

n = 20 Years          

So,

So, The recipient of this settlement has the option of accepting $70,908 as the present value of this payment stream as a single lump sum payment.