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Question

What is the cost for a 2 week delay on a $30 million project based on a 9% interest rate?

Solution

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Question

What is the cost for a 4 day delay on a $50 million project based on a 9% interest rate?

What is the cost for a 2 week delay on a $30 million project based on a 9% interest rate?

Solution

The given questions relates to Continuous Compounding Interest. As the project delays the cost increases due to the factor of inflation and interest.

The addition of interest to the principal sum is called Compounding. Compounding Interest is interest on Interest

Formula of Continuous Compounding can be used to calculate cost of delay

Cost of Delay = PV * e^rt - PV

Here, PV = Present cost of project

e = the mathematical constant r = annual rate of interest t = time in terms of years

By this formula

PART I

PV = $ 50 million

r = 9 % or 0.09

t = 4 days or 4/360 days or 0.0111 year

Cost of delay = PV * e^rt - PV

= 50 × e^(0.09*00.0111) - 50

= 50 * e^0.001 - 50

{Taking value of e^0.001 from

Continuous compounding Table.

e^0.001 = 1.001}

= 50 * 1.001 - 50

= 50.05 - 50

= $ 0.05 Million

Therefore Cost of delay would be $0.05 million if project delayed by 2 days.

PART II

PV = $ 30 millon

r = 9% or 0.09

t = 2 weeks or 2weeks/52weeks or 0.03846 year

Cost of delay = PV * e^rt - PV

= 30 * e^(0.09*0.03846) - 30

= 30* e^0.003461 - 30

{ value of e^0.003461 in continuous compounding table is 1.003 (approx)}

= 30 * 1.0035 - 30

= 30.10 - 30.00

= $ 0.10 million

Therefore cost of delay if project delays by 2 weeks will be

$0.10 million.

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