ENGINEERING ECONOMY PROBLEMS

Class Problem 1 - We learned in class that if we want to have $5,000,000 when we retire in 50 years, and our money will earn 10% interest, then we need to put $42,593 in the bank now. However, we realized that we don't have that much money. If we commit to saving some money every month between now and retirement, then how much do we need to save monthly to have $5,000,000 at the end of 50 years? Again, assume a 10% interest rate.

int10%

12

n_per 5012

FV 5000000

AFVint

1 int( )n_per

286.63

Class Problem 2 - Dr. Swanbom has just won $100,000,000 in the lottery and is about to resign his position at the university. Before he does, he needs some financial advice from his ENGR 122 students. Should he (1) take the $100,000,000 in the form of annual payments of $5,000,000 for the next 20 years, or (2) take $40,000,000 as a lump sum payment now? Assume that with both options he won't spend any of the money, but will instead invest all of it at 9% interest compounded yearly. Neglect the effect of taxes on both options.

FV1 50000001 9%( )

201

9%

FV1 255.8 106

FV2 40000000 1 9%( )20

FV2 224.18 106

difference FV1 FV2 31.62 106

He should take option 1, because it will yield $31,620,000 more.

Class Problem 3 - Dr. Cronk is considering whether or not to re-finance the mortgage on his home. He owes $100,000 on his home, and will continue paying the mortgage for the next 25 years. He currently is paying 7% interest on the mortgage. (a) What are his current monthly payments? (b) How much interest will he pay over the next 25 years if he keeps his present mortgage? (In other words, how much does his current loan cost?) If Dr. Cronk re-finances the home, he will have to pay the mortgage company $4,000 for the costs of refinancing the loan. The company will add that to his balance, so that he will owe $104,000 on the house. However, the interest rate will drop to 6.5%. Assuming that Dr. Cronk re-finances for 25 years, then: (c) What will his new monthly payment be? (d) How much will his new loan cost? (Hint: Include interest charges and the cost of refinancing.) (e) Should Dr. Cronk keep his current loan or re-finance his home? Why?

Part A

inta7%

12

Aa 100000inta 1 inta 12 25( )

1 inta 12 25( )1

Aa 706.78 payments Dr. Cronk is currently making each month.

Part B

total_interest a Aa 12 25 100000 112034

Part C

intc6.5%

12

Ac 104000intc 1 intc 12 25( )

1 intc 12 25( )1

Ac 702 monthly payments Dr. Cronk will make for the new loan

Part D

loan_cost d 4000 Ac 12 25 104000

loan_cost d 110665

Part E

diff total_interesta loan_cost d 1369

Dr. Cronk should consider taking the loan because, even though he will have to pay $4000 more for the house, he will still save $1,369 by the time he finishes paying the mortgage. However, the paperwork for re-financing the home is a pain to fill out; he may want to wait to see if mortgage rates drop further before making his decision.

Class Problem 4 - The Biomedical Engineering Program is interested in purchasing a new scanning electron microscope (SEM). The cost of the microscope is $50,000; however, the prices have been dropping at the rate of about 5% per year. The program can set aside about $8000 annually into an account that will accrue interest at 10%. How long will it be before BME can purchase the microscope?

FVmicroscope n( ) 50000 1 5%( )n

50000 1 5%( )5

38689

50000 1 5%( )5

39176

FVsavings n( ) 80001 10%( )

n1

10%

n 1 5

1 2 3 4 50

1 104

2 104

3 104

4 104

5 104

FVmicroscope n( )

FVsavingsn( )

n

According to the graph, we will need to save for 5 years to make the purchase. By that time, we should have

diff FVsavings 5( ) FVmicroscope 5( ) 10152

or $10,152 more than we need.