Probability and Engineering Economy
For full credit please show all your work and explain your answers
1. You deposit $3,000 in a savings account.
a. How many years do you need to double your money if your account earns 9% simple
interest (not compounded) per year?
b. If you deposit the $3,000 in another savings account that earns 8% interest, compounded
yearly, how many years will take to double your money?
2. You are considering investing $1,000 at interest rate of 6%, compounded annually, for 5
years or investing the $1,000 at 7% per year simple interest rate for 5 years. Which option is
better?
3. Suppose you have the option of receiving either $10,000 at the end of 5 years or P dollars
today. Currently you have no need for money, so you would deposit the P dollars in a bank
that pays 6% interest. What value of P would make you indifferent in your choice between P
dollars today and the promise of $10,000 at the end of 5 years?
4. You can buy a machine for $100,000 that will produce a net income, after operating
expenses, of $10,000 per year. If you plan to keep the machine for four years, what must the
market (resale) value be at the end of four years to justify the investment? Assume 15%
annual return on the investment (interest rate).
5. The Rule of 72 can be used to find (approximately) the time required to double an
investment for a given interest rate. The rule is as follows:
Rule of 72: The time required to double the value of a lump-sum
investment that is allowed to compound is approximately
72 divided by the annual interest rate (as a %)
Use the Rule of 72 to determine how long it takes to accumulate $10,000 in a savings
account when P = $5,000 and i = 10% per year. Find the actual value using the appropriate
formula and compare the two results.
6. Answer the following questions:
a. What equal annual series of payments must be paid to accumulate $12,000 in 13 years at
5%, compounded annually?
b. Part of the income a machine generates is put into a fund to finance the purchase of a
new machine. If $1,500 is invested annually at 7% interest (compound) how many years
before the fund becomes $25,000?
c. What is the future value of the following series of payments: $1,000 for 5 years at 8.25%?
7. A local newspaper headline blared: “Bo Smith signed for $30 Million.” A reading of the
article revealed that Bo Smith, the former record-breaking running back from Football
University, signed a $30 million package with the Dallas Stars. The terms of the contract
were: $3 million signing bonus paid immediately, $2.4 million per year for the first 5 years
(first payment after 1 year) and $3 million per year for next 5 years (first payment at year 6).
If the interest rate is 8% per year,
a. Show the cash flow.
b. Find the present value of the contract.
8. Maintenance costs for a small bridge with an expected 50-year life are estimated to be $1,000
each year for the first 5 years, followed by $10,000 expenditure in the year 15 and $10,000
expenditure in year 30. If i = 10% per year, what is the present value?
9. A loan company lends money at 1.5% per month, compounded monthly.
a. What is the nominal interest rate (annual)?
b. What is the effective annual interest rate?
c. How many years will it take an investment to triple itself if interest is compounded
monthly?