Survey equipment is very expensive and become obsoletes and needs to be replaced

Question

Survey equipment is very expensive and become obsoletes and needs to be replaced every 5 years. Consider a new GPS system consisting of a base station ($18,968 today's cost), a rover ($7665 today's cost), and software ($3833 today's cost). If the survey firm can put $485 in the bank each month in a savings account that will earn 3% APR, compounded monthly, will they have enough money in the account at the end of 5 years to to cover the cost of the new equipment if the cost of the equipment will be 4% higher in 5 years when they want to purchase the new equipment?

Explanation / Answer

Cost the equipment today = ($18,968 today's cost) + a rover ($7665 today's cost) +software ($3833 today's cost).

Cost the equipment today = $ 30,466

cost the of the equipment at end of 5 years =  $ 30,466 + 0.04X $ 30,466 = $ 31,684.64

The amount at end of 60 months = 31,432.20

Hence the amount is not sufficient to buy the GPS unit.

The calculation using excel is shown below.

Month End of the month amount Interest 1 486.215 1.0025 2 487.4305 1.0025 3 488.6491 1.0025 4 489.8707 1.0025 5 491.0954 1.0025 6 492.3232 1.0025 7 493.554 1.0025 8 494.7878 1.0025 9 496.0248 1.0025 10 497.2649 1.0025 11 498.508 1.0025 12 499.7543 1.0025 13 501.0037 1.0025 14 502.2562 1.0025 15 503.5118 1.0025 16 504.7706 1.0025 17 506.0326 1.0025 18 507.2976 1.0025 19 508.5659 1.0025 20 509.8373 1.0025 21 511.1119 1.0025 22 512.3897 1.0025 23 513.6706 1.0025 24 514.9548 1.0025 25 516.2422 1.0025 26 517.5328 1.0025 27 518.8266 1.0025 28 520.1237 1.0025 29 521.424 1.0025 30 522.7276 1.0025 31 524.0344 1.0025 32 525.3445 1.0025 33 526.6578 1.0025 34 527.9745 1.0025 35 529.2944 1.0025 36 530.6177 1.0025 37 531.9442 1.0025 38 533.2741 1.0025 39 534.6072 1.0025 40 535.9438 1.0025 41 537.2836 1.0025 42 538.6268 1.0025 43 539.9734 1.0025 44 541.3233 1.0025 45 542.6766 1.0025 46 544.0333 1.0025 47 545.3934 1.0025 48 546.7569 1.0025 49 548.1238 1.0025 50 549.4941 1.0025 51 550.8678 1.0025 52 552.245 1.0025 53 553.6256 1.0025 54 555.0097 1.0025 55 556.3972 1.0025 56 557.7882 1.0025 57 559.1827 1.0025 58 560.5806 1.0025 59 561.9821 1.0025 60 563.387 1.0025 31432.2

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