Question 2.3: The ABC Company is to receive $1 a period for three periods,...
The ABC Company is to receive $1 a period for three periods, the first payment to be received one period from now. The time value factor is 0.10. Compute the present value of the annuity.
There are three equivalent solutions:
a. From Appendix Table B,
B(3, 0.10) = 2.4869.
b. Using equation (2.6) and Appendix Table A,
B(n,r) =\frac{1-(1+r)^{-n} }{r} (2.6)
B(3, 0.10) =\frac{1-(1+r)^{-n} }{r} =\frac{1-0.7513}{0.10}=\frac{0.2487}{0.10}=2.487
c. Adding the first three entries in the 0.10 column in Appendix Table A,
(1.10)^{-1} = 0.9091
(1.10)^{-2} = 0.8264
(1.10)^{-3} = \underline{0.7513}
B(3, 0.10) = 2.4868.
If, instead of $1 per period, the amount is $100.00, then using equation (2.7),
PV = C × B(n , r). (2.7)
we would multiply $2.487 by $100.00 and obtain $248.70.