Question 1

Which of the following best explains why a dollar received today is worth more than a dollar received one year from now?

Accepted Answer

Because money received today can be invested to earn a return, increasing its future value.

Question 2

If you invest $$1,000 at an annual interest rate of 10% compounded annually for 3 years, what will be the future value (FV) of your investment? Use the formula FV = P(1+i)^N$.

Accepted Answer

$$FV = 1000(1+0.10)^3$ = 1331$$

Question 3

Which formula correctly calculates the present value (PV) of a future sum $$F$$ received in $$N$$ years at an interest rate $$i$$?

Accepted Answer

$$PV = \frac{F}{(1+i)^N}$$

Question 4

A company expects to need $$100,000 in 13 years for a project. If the annual interest rate is 8%, how much should they invest today? Use PV$$ = \frac{FV}{(1+i)^N}$.

Accepted Answer

$$PV = \frac{100,000}{(1.08$$)^{13}$$} = 36,769.79$$

Question 5

Which of the following statements about compound interest is TRUE?

Accepted Answer

Interest is calculated on both the original principal and the accumulated interest from previous periods.

Question 6

If the nominal interest rate is 8% per year, compounded quarterly, what is the effective annual interest rate? Use $$i_{effective} = (1 + \frac{0.08}{4})^4$ - 1.$$

Accepted Answer

$$i_{effective} = (1 + 0.02)^4$ - 1 = 0.0824 or$$ $$8.24\%$$

Question 7

Which cash flow type is best described as a series of equal payments made at regular intervals?

Accepted Answer

Uniform series (Annuity)

Question 8

A project requires an initial investment of $$80,000 and generates annual cash inflows of 12$$,000 for 6 years. If the interest rate is 8%, what is the future value (FV) of these inflows at the end of year 6? Use $$FV = A \left[ \frac{(1+i)^N - 1}{i} \right].$$

Accepted Answer

$$FV = 12,000 \left[ \frac{(1.08)^6$ - 1}{0.08} \right] = 93,305.28$$

Question 9

Which of the following is NOT a typical category of cash flow in engineering projects?

Accepted Answer

Depreciation expense

Question 10

A company borrows $10,000 at 8% interest, repaying half the principal plus interest at the end of year 1, and the rest at the end of year 2. What is the total amount paid at the end of year 1?

Accepted Answer

$$5,800$$ ($$5,000$$ principal + $$800$$ interest)

Question 11

Which formula is used to calculate the future value with continuous compounding?

Accepted Answer

$$F = Pe$$^{rt}$$

Question 12

If inflation exceeds the earning rate on an investment, what happens to the purchasing power of your money?

Accepted Answer

Purchasing power decreases.

Question 13

Which of the following best describes economic equivalence?

Accepted Answer

Two cash flows are economically equivalent if they have the same value at different points in time, adjusted for interest rate.

Question 14

A cash flow diagram shows a $$20,000$$ outflow at time 0, followed by five annual inflows of $$4,000$$ and a final inflow of $$11,000 at $$year 5. What is the net cash flow at year 5?

Accepted Answer

$$11,000$$

Question 15

Which of the following is a correct formula for the present value of an uneven series of payments?

Accepted Answer

$$PV = \sum_{k=1}^{N} \frac{P_k}{(1+i$$)^{k}$$}$$

Question 16

Which of the following is NOT a use of cash flow analysis in engineering economics?

Accepted Answer

Calculating the depreciation schedule for tax purposes.

Question 17

If you are comparing two investment plans with different cash flows, what must you do to make a fair comparison?

Accepted Answer

Discount all cash flows to a common point in time using the same interest rate.

Question 18

Which of the following best describes the difference between nominal and effective interest rates?

Accepted Answer

Effective rate includes compounding, nominal rate does not.

Time Value of Money, Interest Rates, and Cash Flow Analysis: Mini-Textbook Study Notes

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