The city of Suburbia received a proposal for plant watering from Water Can Garde

Question

The city of Suburbia received a proposal for plant watering from Water Can Gardening Company. The company would water all city plants for $510 each quarter, increasing the amount charged by $18 each subsequent quarter. Water Can Gardening Company requires a 7-year commitment. The mayor has asked you to calculate the equivalent uniform quarterly cost for the plant water service to help with budgeting. Use a nominal annual interest rate of 5%, compounded quarterly, to make the calculation. Enter your answer as follows: 12345 Round your answer. Do not use a dollar sign ("$"), any commas ("") or a decimal point (")

Explanation / Answer

Quarterly nominal interest rate = 5% / 4 = 1.25%

Number of quarters = 7 x 4 = 28

First, we compute Present Worth of costs as follows. Note that

Equivalent uniform quarterly cost ($) = Present worth / P/A(1.25%, 28) = 17355 / 23.5025** = 738

**P/A(r%, N) = [1 - (1 + r)-N] / r

P/A(1.25%, 28) = [1 - (1.0125)-28] / 0.0125 = (1 - 0.7062) / 0.0125 = 0.2938 / 0.0125 = 23.5025

Quarter Cost ($) PV Factor @1.25% Discounted Cost ($) (A) (B) (A) x (B) 1 510 0.9877 504 2 528 0.9755 515 3 546 0.9634 526 4 564 0.9515 537 5 582 0.9398 547 6 600 0.9282 557 7 618 0.9167 567 8 636 0.9054 576 9 654 0.8942 585 10 672 0.8832 593 11 690 0.8723 602 12 708 0.8615 610 13 726 0.8509 618 14 744 0.8404 625 15 762 0.8300 632 16 780 0.8197 639 17 798 0.8096 646 18 816 0.7996 652 19 834 0.7898 659 20 852 0.7800 665 21 870 0.7704 670 22 888 0.7609 676 23 906 0.7515 681 24 924 0.7422 686 25 942 0.7330 691 26 960 0.7240 695 27 978 0.7150 699 28 996 0.7062 703 Present Worth ($) = 17355

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