An engineer wants to build a software program company that requires multiple inv
ID: 1093817 • Letter: A
Question
An engineer wants to build a software program company that requires multiple investments over the next 10 years. Annual operation and maintenance costs are expected to be $50,000 per year. The company will also need a new technology development program to start in the sixth year of operation. The cost of the new program will be $50000 at the start of the program, and reduced by $10000 every year after. The bank has agreed to lend her the money for this business at 10% interest. How much is the future value of her loan?
Explanation / Answer
FV of maintenance cost,
FV = PV ( 1+rate/100)^T
FV = 50000 [( 1 + 10/100)^1 +( 1 + 10/100)^2 +.........+( 1 + 10/100)^10]
= 50000*1.1*[ 1 + 1.1 + (1.1)^2+ ...... + (1.1)^9]
= 55000*[ {(1.1)^10 -1}/ (1.1-1)}] = $876558.35
For development program,
FV = 50000*(1.1)^5 + 40000*(1.1)^4+ 30000*(1.1)^3 + 20000*(1.1)^2 + 10000*(1.1)^1
1.1 = ( 1+ rate/100)
FV = $214219.5
Total future value = $1090777.85