Question

This question about " Engineering Economics ".

Notes:

- Use standard notation equations

- Draw cashflow diagram

Question: A growing machine shop wishes to set aside money now to invest over the coming years in automating its customer service department. The company can earn 10% on a lump sum amount deposited now, and it wishes to do the following:

* Year 1 - no expenses

* Year 2 - withdraw $25,000 purchase computers and database software

* Year 3 - withdraw $3,000 to purchase additional software

* Year 4 - deposit $1,000 from the income

* Year 5 - withdraw $5,000 to purchase software updates

How much money must be deposited now in order to cover the expected payments over the next five years? Assume that all the transactions are made at the beainning of each year.

O -$27,870.36

O -$29,372.98

O $27,870.36

O $29,372.98

Answer 1

Let the amount to be invested today be X

Deposit today X

At the end of 1^st year = X*1.1 = 1.1X

___

Withdraw 25,000 at the start of 2^nd year

Balance at the end of 2^nd year

=> (1.1X - 25,000) * 1.1

=> 1.21X - 27,500

___

Withdraw 3,000 at the beginning of 3^rd year

Balance at the end of 3^rd year

=> (1.21X - 27,500 -3,000) * 1.1

=> 1.331X -33,500

___

Deposit 1,000 in the beginning of 4^th year

Balance at the end of 4^th year

=> (1.331X - 33,500 + 1,000) * 1.1

=> 1.4641 X -35,805

___

At the start of the 5^th year, balance must be 5,000

=> 1.4641X - 35,850 = 5,000

=> 1.4641X = 5,000 + 35,805

=> X = 40,805 / 1.4641

=> X= $27.870.36

So the initial deposit is $27,870.36

Option C