Q. A lottery ticket states that you will receive $250 every year for the next ten years.

a.What is the value of the winning lottery ticket in present value if the discount rate is 6%, and it is an ordinary annuity?

b.What is the value of the winning lottery ticket in present value if the discount rate is 6%, and it is an annuity due?

c.What is the difference between the ordinary annuity and annuity due in parts (a) and (b)?

d.Verify that the difference in part (c) is the difference between the $250 first payment of the annuity due and the discounted final $250 payment of the ordinary annuity.

ANSWER

Answer with calculator: (settings are P/Y = 1, C/Y = 1, and END mode)

Part a.

INPUT106.0?$250$0

VariablesNI/YPVPMTFV

OUTPUT$1,840.02

Reset Calculator to BGN mode

Part b.

INPUT106.0?$250$0

VariablesNI/YPVPMTFV

OUTPUT$1,950.42

Part c.

Difference is $1,950.42 - $1,840.02 = $110.40

Part d.

Verification with the two different timed payments, first for annuity due and last for ordinary annuity:

Difference= $250.00 - $250.00 1/1.06¹⁰

= $250.00 - $250.00 x0.5584

= $250.00 - $139.60 = $110.40

My Question:

Can someone please help me understand part d? what is the meaning of it and how can we get it using a financial calculator?

Thank you,