Your company has won a contract to build a large Headquarters office on land rec

Question

Your company has won a contract to build a large Headquarters office on land reclaimed from the sea, off the North Queensland Coast. Management has estimated that the main heavy plant required for the contract will be:

Plant

Quantity

unit cost

off-highway haul trucks

2

$86000 per truck

front end bucket loaders

4

$83000 per loader

backhoe hydraulic excavators

2

$78000 per excavator

piling rigs

4

$140000 per pile rig

bulldozers with attachments

2

$132000 per bulldozer

Due to the duration of the project, which is estimated as 3 years, senior management has instructed that these plant items be bought. You have made enquiries with the company bank and they will loan the required amount at a fixed rate of interest 6 % per annum. The company will be making monthly repayments on the loan and interest on the loan will be compounded monthly.

How much will the company have to repay the bank each month in order to clear the debt after 3 years?

(Round your answer to the nearest dollar. Do not include the dollar sign or any spaces or commas.)

Plant

Quantity

unit cost

off-highway haul trucks

2

$86000 per truck

front end bucket loaders

4

$83000 per loader

backhoe hydraulic excavators

2

$78000 per excavator

piling rigs

4

$140000 per pile rig

bulldozers with attachments

2

$132000 per bulldozer

Explanation / Answer

The loan is for 1484000.

The interest rate is .06/12 = .005

Then, if the monthly payment is P,

P/1.005 + P/1.005^2 + ...+P/1.005^36 = 1484000

The geometric sum formula for a finite sum is a (1 - r^n)/(1-r), where a is the first term and r is the ratio.

Here, the ratio is 1/1.005 and the first term is Pr

Then, the sum is Pr(1-r^n)/(1-r) = P(1/1.005)(1-(1/1.005)^36)/(1-1/1.005)

Not that it makes much difference, but we can divide 1/.005 by (1-1/1.005) = 1/1.005/(.005/1.005) =

1/.005

Then, we have P(1/.005)(1-(1/1.005)^36) = 1484000

Then, P = 1484000 * .005/(1-(1/1.005)^36) = 45146.16

Note that we can check this via Excel. The last payment is 20 cents less. Each month, the interest is .005 * the previous month's balance, the principal paid is the payment - the interest, and this is the amount deducted from the balance.

Month Balance Payment Interest Principal 0 1484000.00 1 1446273.84 45146.16 7420.00 37726.16 2 1408359.05 45146.16 7231.37 37914.79 3 1370254.69 45146.16 7041.80 38104.36 4 1331959.80 45146.16 6851.27 38294.89 5 1293473.44 45146.16 6659.80 38486.36 6 1254794.65 45146.16 6467.37 38678.79 7 1215922.46 45146.16 6273.97 38872.19 8 1176855.91 45146.16 6079.61 39066.55 9 1137594.03 45146.16 5884.28 39261.88 10 1098135.84 45146.16 5687.97 39458.19 11 1058480.36 45146.16 5490.68 39655.48 12 1018626.60 45146.16 5292.40 39853.76 13 978573.57 45146.16 5093.13 40053.03 14 938320.28 45146.16 4892.87 40253.29 15 897865.72 45146.16 4691.60 40454.56 16 857208.89 45146.16 4489.33 40656.83 17 816348.77 45146.16 4286.04 40860.12 18 775284.35 45146.16 4081.74 41064.42 19 734014.61 45146.16 3876.42 41269.74 20 692538.52 45146.16 3670.07 41476.09 21 650855.05 45146.16 3462.69 41683.47 22 608963.17 45146.16 3254.28 41891.88 23 566861.83 45146.16 3044.82 42101.34 24 524549.98 45146.16 2834.31 42311.85 25 482026.57 45146.16 2622.75 42523.41 26 439290.54 45146.16 2410.13 42736.03 27 396340.83 45146.16 2196.45 42949.71 28 353176.37 45146.16 1981.70 43164.46 29 309796.09 45146.16 1765.88 43380.28 30 266198.91 45146.16 1548.98 43597.18 31 222383.74 45146.16 1330.99 43815.17 32 178349.50 45146.16 1111.92 44034.24 33 134095.09 45146.16 891.75 44254.41 34 89619.41 45146.16 670.48 44475.68 35 44921.35 45146.16 448.10 44698.06 36 0.00 45145.96 224.61 44921.35

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