The ABC Company is to receive $1 a period for three periods, the first payment to be

Question:

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.

Data from  Appendix Table B

n/r 1% 10% 11% 12% 13% 14% 15% 1 2 1.9704 1.9416 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259

n/r 1% 21 18.8570 17.0112 15.4150 14.0292 12.8211 11.7641 10.8355 10.0168 22 19.6604 17.6580 15.9369 14.4511

n/r 16% 1 0.8621 0.8475 0.8333 0.8197 0.8065 0.7937 0.7813 0.7692 0.7576 0.7463 0.7353 0.7246 0.7143 0.6897

Table B (Continued) n/r 16% 21 5.9731 5.3837 4.8913 4.4756 4.1212 3.8161 3.5514 3.3198 3.1158 2.9349 2.7734

b. Using equation (2.6) and Appendix Table A,

B(3,0.10) 1- (1+r)-n = 10.7513 0.10 = 0.2487 0.10 = = 2.487.

Data from equation  (2.6)

B(n,r) 1- (1+r)-n r

Data from Appendix Table A

1% 2% 3% 4% Table A Present value of $1.00 (1 + r)". 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 1 0.9901 0.9804

1% 10% 11% 12% 13% 14% 15% 16 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 0.1883

n/r 16% 18% 20% 22% 24% 26% Table A (Continued) 28% 30% 32% 34% 36% 38% 40% 45% 50% 1 0.8621 0.8475 0.8333

18% 20% 22% 24% n/r 16% 21 0.0443 0.0309 0.0217 0.0154 0.0109 0.0078 0.0056 0.0040 0.0029 0.0021 0.0016


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 0.7513 B(3, 0.10) 2.4868. =

If, instead of $1 per period, the amount is $100.00, then using equation (2.7), we would multiply $2.487 by $100.00 and obtain $248.70.

Data from equation (2.7)

PVC x B(n,r)

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