Finance Homework Questions on Present Value, Future Value, Annuities, and Perpetuities

• Show any and all work necessary. You can receive partial credit for wrong answers if you write out correct formulas and show work.
• This homework should be nicely handwritten
• Remember to explain all your steps and to show all formulas you use before you put numbers into the equations.
o First, write the formula
o Second, substitute the numbers into the formula
o Third, say what is left to compute
o Fourth, compute
• Each question is worth 20 points. (total: 140 points)
• Note: In some questions, you may need to use more than one formula. In this case, repeat the  steps previously mentioned.
Question 1 
An art collector has the opportunity to invest in paintings; the investment requires an outlay of $2 million. He is certain that he will be able to sell the paintings for $2.18 million in one year. He 
also has the opportunity to invest in certificates of deposit (CDs) which pay 10% per year. 
(1.1) What is the FV of the $2 million if the collector purchases the CDs? 
(1.2) Is the investment in the paintings a good investment?
(1.3) What is the rate of return for the investment paintings?
Question 2
The cash inflow from this investment will be $114 one year from today (year 1) and $144 two 
years from today (year 2). The market rate of interest is 20%. 
(2.1) Find the present value (PV) for this investment. 
(2.2) If the initial outlay is $195, is the investment acceptable?
Question 3
Compute the following based on the charts (make sure to show your work per computation-recall the directions):
(3.1) Compute Present Value
Future Value Years Interest Rate Present Value $ 498 7 13%
(3.2) Compute Future Value
Present Value Years Interest Rate Future Value $ 123 13 13% 
(3.3) Unknown time period
Present Value Future Value Interest Rate Time (years) $ 100 $ 348 12%
(3.4) Interest Rate
Present Value Future Value Interest Rate Time (years) $ 100 $ 466 20
(3.5) Calculate the effective annual rate (EAR) APR Stated Rate Number of times  compounded Effective Rate 5% Semiannually
Question 4
Consider a perpetuity that pays $100 per year. The market rate of interest is 10%. 
(4.1) What is the PV of the perpetuity? 
(4.2) What is the PV of the perpetuity three years from now? 
(4.3) What is the present value of the perpetuity “n” years from now? 
(4.4) Under what circumstances does the value of a perpetuity change?
Question 5
Compute:
(5.1) Compute the present values of the following ordinary annuities Payment Years Interest Rate Present Value
$ 678.09 7 13%
7,968.26 13 6
20,322.93 23 4
(5.2) Compute the future values of the following ordinary annuities Payment Years Interest Rate Future Value
$ 123 13 13%
4,555 8 8
74,484 5 10
Question 6
Define the following terms in no more than one sentence.
(6.1) Compound interest
(6.2) Discount rate
(6.3) Future value
(6.4) Present value
(6.5) Simple interest
(6.6) Annual Percentage Rate (APR)
(6.7) Annuity due
(6.8) Effective Annual Rate (EAR)
(6.9) Perpetuity
(6.10) Stated interest rate
Question 7
For the following, fill in the blanks with the appropriate term(s). For questions that give you two or three choices to choose from, circle the most appropriate.
(7.1) __________________ means earning interest on interest, so we call the result _____________. _________________ refers to the amount of money an investment will grow  to over some period of time at some given interest rate. The future value (FVt) of an initial  deposit (PV) which earns interest at the rate r for t years is given by the following formula: 
FVt = ________________. The expression (formula) is sometimes called the future value interest factor for $1 invested at r percent for t periods and can be abbreviated as ________________.
(7.2) A present value is the amount which must be invested today, at a specified, to grow the initial investment to a specified _______________ at a  specified . The PV is depended on three values: the _________________, the amount of the , and the __________________. The rate used in the calculation of a present value is called .
(7.3) The basic PV equation as follows: PV = _______________. Or, we can rearrange the basic PV equation, so the PV is determined by multiplying the future value (FV) times the _______________ of the FV interest factor: PV = . The term [1/(1+r)t] is called the present value interest factor and is abbreviated ______________. The PVIF is also called the and calculating the present value of a future cash flow to determine its worth today is commonly called ________________________ valuation. 
(7.4) A FV with multiple cash flows can be computed by finding the _____________________of each deposit and then summing the separate . A PV with multiple  cash flows can be calculated by separately computing the of each cash flow and then summing the separate . 
(7.5) An annuity is a series of cash flows that occur at of each period for some ______________ number of periods. When the payments occur at the end of the time period, the annuity is referred to as an annuity form. If payments are at the beginning of the time period, we call the annuity an 
(7.6) The PV of an annuity formula is: C x {_____________________}, where the term in parentheses is sometimes called the ______________________________________________ and abbreviated ___________________.
(7.7) The FV of an annuity formula is: C x {_____________________},where the term in parentheses is sometimes called the _____________________________________________.
(7.8) A perpetuity is an annuity with the ____________ stream of cash flows continuing _______________. The PV of a perpetuity formula is PV = _________________. The formula can also be solved for C and written as: C = __________________. It can also be solved for r: r = ___________________.
(7.9) The interest rate expressed in terms of the interest payment made each period is called a ______________ interest rate or a ______________ interest rate. When interest rate is compounded more than once a year, the actual interest rate is than the quoted interest rate. The actual interest rate is called the __________________________. The aforementioned interest rate can be computed as follows: {[1 + (_______________)] -1}, where m is the number of times per year interest is compounded. When interest is compounded m times per year, the future value equals (equation) . 
(7.10) The three basic types of loans are pure loans, interest-only loans, and amortized loans. A pure discount loan is a loan with which the borrower receives money today and repays a ______________ at some time in the future. The second type of loan repayment plan, called interest-only loans, calls for the borrower to pay ____________ each period and to repay the entire _____________ at some point in the future. An amortized loan requires that the borrower to repay parts of the loan amount over time; i.e. the borrower make periodic payment which include both __________ and repayment of a portion of the ___________. Notice that the interest paid in this case (grows / declines) each period, because the loan balance is going down.