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Unformatted text preview: Chapter 2 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 2-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest. PV is also the beginning amount that will grow to some future value. The parameter i is the periodic interest rate that an account pays. The parameter INT is the dollars of interest earned each period. FV n (future value) is the ending amount in an account, where n is the number of periods the money is left in the account. PVA n is the value today of a future stream of equal payments (an annuity) and FVA n is the ending value of a stream of equal payments, where n is the number of payments of the annuity. PMT is equal to the dollar amount of an equal, or constant cash flow (an annuity). In the EAR equation, m is used to denote the number of compounding periods per year, while i Nom is the nominal, or quoted, interest rate. b. FVIF i,n is the future value interest factor for a lump sum left in an account for n periods paying i percent interest per period. PVIF i,n is the present value interest factor for a lump sum received n periods in the future discounted at i percent per period. FVIFA i,n is the future value interest factor for an ordinary annuity of n periodic payments paying i percent interest per period. PVIFA i,n is the present value interest factor for an ordinary annuity of n periodic payments discounted at i percent interest per period. All the above factors represent the appropriate PV or FV n when the lump sum or ordinary annuity payment is $1. Note that the above factors can also be defined using formulas. c. The opportunity cost rate (i) of an investment is the rate of return available on the best alternative investment of similar risk. d. An annuity is a series of payments of a fixed amount for a specified number of periods. A single sum, or lump sum payment, as opposed to an annuity, consists of one payment occurring now or at some future time. A cash flow can be an inflow (a receipt) or an outflow (a deposit, a cost, or an amount paid). We distinguish between the terms cash flow and PMT. We use the term cash flow for uneven streams, while we use the term PMT for annuities, or constant payment amounts. An uneven cash flow stream is a series of cash flows in which the amount varies from one period to the next. The PV (or FV n ) of an uneven payment stream is merely the sum of the present values (or future values) of each individual payment. Mini Case: 2 - 1 e. An ordinary annuity has payments occurring at the end of each period. A deferred annuity is just another name for an ordinary annuity. An annuity due has payments occurring at the beginning of each period. Most financial calculators will accommodate either type of annuity. The payment period must be equal to the compounding period....
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