Engineering Economics practice questions

Answer: C) $38,697

A single present amount grows by the single-payment compound amount factor: F = P(1 + i)^n = 10,000(1.07)^20 ≈ $38,697.

• AIncorrect. This is 10,000(1.07)^10, which compounds over only 10 periods instead of 20.
• BIncorrect. This is 10,000(1 + 0.07 × 20), which is simple interest. The account compounds annually, so each year's interest also earns interest.
• CCorrect. F = P(F/P, 7%, 20) = 10,000(1.07)^20 = 10,000(3.8697) ≈ $38,697.
• DIncorrect. This uses the uniform-series compound amount factor (F/A, 7%, 20) = 40.9955. That factor applies to $10,000 deposited every year, but here there is only one deposit.

Answer: A) 8 years

• ACorrect. Divide 72 by the 9% rate.
• BIncorrect. Divide 72 by the rate.
• CIncorrect. Recheck the division.
• DIncorrect. That's at 6%.

Answer: B) $10,795

• AIncorrect. That's simple interest.
• BCorrect. \(5{,}000(1.08)^{10} = 5{,}000(2.1589)\).
• CIncorrect. That's one year.
• DIncorrect. Recheck the compound factor.

Answer: B) $12,578

End-of-year deposits form an ordinary annuity: F = A(F/A, 5%, 10) = 1,000 × 12.578 ≈ $12,578.

• AIncorrect. This is just the sum of the deposits and leaves out all interest earned.
• BCorrect. F = A[(1 + i)^n − 1]/i = 1,000 × (1.6289 − 1)/0.05 = 1,000 × 12.578 ≈ $12,578.
• CIncorrect. This is the annuity-due result, 12,578 × 1.05, which applies to deposits made at the start of each year. Here the deposits are made at the end of each year.
• DIncorrect. This compounds the full $10,000 for 10 years as one lump sum, 10,000 × (1.05)^10. In fact, each deposit earns interest only for the years remaining after it is made.

Answer: B) $2,500

• AIncorrect. That's the after-tax remainder.
• BCorrect. Depreciation × tax rate.
• CIncorrect. Multiply by the tax rate.
• DIncorrect. Multiply, don't divide.

Answer: B) $35,000

• AIncorrect. Subtract salvage before dividing by life.
• BCorrect. Annual depreciation $5,000; 50,000 − 15,000.
• CIncorrect. That's accumulated depreciation.
• DIncorrect. Recheck the depreciation.

Answer: A) 2,000 hours a year

• ACorrect. $20,000 ÷ $10 per hour.
• BIncorrect. That's off by a factor of 10.
• CIncorrect. That ignores the hourly savings.
• DIncorrect. That isn't the calculation.

Answer: C) 1.00%

For a nominal rate r compounded m times per year, the rate per period is r/m. Here that is 12%/12 = 1% per month. The effective annual rate is (1.01)^12 − 1 ≈ 12.68%.

• AIncorrect. This is 12%/4, the rate per quarter. Compounding here is monthly, so there are 12 periods per year.
• BIncorrect. This is (1.12)^(1/12) − 1, the monthly rate that would give a 12% effective annual rate. The 12% here is a nominal rate, so you simply divide it by the number of periods.
• CCorrect. The rate per period equals the nominal rate divided by the number of compounding periods per year: 12%/12 = 1% per month.
• DIncorrect. This is the effective annual rate, (1.01)^12 − 1 ≈ 12.68%. It is a yearly rate, not a rate per month.

Answer: A) $8,718

To turn a present cost into an equal annual cost, multiply by the capital recovery factor: (A/P, 6%, 20) = 0.08718, so A ≈ $8,718 per year.

• ACorrect. A = P(A/P, 6%, 20) = 100,000 × 0.06(1.06)^20/[(1.06)^20 − 1] = 100,000 × 0.08718 ≈ $8,718.
• BIncorrect. $100,000 / 20 spreads the cost evenly and ignores the time value of money.
• CIncorrect. 6% of $100,000 is the yearly interest alone. It leaves out repayment of the $100,000 itself.
• DIncorrect. This uses the sinking fund factor (A/F, 6%, 20) = 0.02718, which turns a future amount into annual payments. A present cost needs the capital recovery factor (A/P).

Answer: A) $2,638

• ACorrect. \(10{,}000(A/P, 10\%, 5) = 10{,}000(0.2638)\).
• BIncorrect. That ignores interest.
• CIncorrect. That's the sinking fund factor.
• DIncorrect. Recheck the factor.