# This key is labeled interest per year but it can

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This key is labeled "interest per year" but it can handle any rate per different compounding periods; for example, ifwe have semiannual interest payments, our compounding periods are semiannual and the interest rate is the semiannual rate. FV Future value of the cash flows, this is a lump sum PMT Annuity (coupon) per discount period PV Present value of the cash flows, this is a lump sum Calculator inputs follow for the three examples in Exhibit 7A.l. In these examples, the unknown value is the price, which is the present value (PV) of the bond's cash flows. (For additional instruction on entering inputs i a specific calculator, or how to do more complicated computations, review the calculator's user manual or revi online calculator tutorials.) Example (1),Exhibit 7A.1: Bond pri.cedto,yield8%. N = 8 (4 years x 2 periods per year = 8 semiannual periods) l/Yr = 4 (8% annual yield -;-2 periods per year = 4% semiannually) FV = 100,000 (face value, which is the lump sum that must be repaid in the future) PMT = 4,000 (\$100,000 x 4% semiannual coupon rate) I PV = 100,000 I (output obtained from calculator) Example (2),Exhibit 7A.1: Bond priced to yield 10%. N=8 IlYr = 5 FV = 100,000 PMT = 4,000 I PV = 93,537 Example (3),Exhibit 7A.1: Bond priced to yield 6%. N=8 IlYr = 3 FV = 100,000 PMT = 4,000 I PV = 107,020 Future Value Concepts Future Value of a Single Amount The future value of a single sum is the amount that a specific investment is worth at a future date if invested given rate of compound interest. To illustrate, suppose that we decide to invest \$6,000 in a savings account pays 60/0 annual interest and we intend to leave the principal and interest in the account for five years. We ass that interest is credited to the account at the end of each year. The balance in the account at the end of five years determined using Table 3 in Appendix A, which gives the future value of a dollar, as follows: Principal x Factor = Future Value \$6,000 x 1.33823 = \$8,029 The factor 1.33823 is at the intersection of the row for five periods and the column for 6%. Next, suppose that the interest is credited to the account semiannually rather than annually. In this situati there are 10 compounding periods, and we use a 3% semiannual rate (one-half the annual rate because there two compounding periods per year). The future value calculation follows: Principal x Factor = Future Value \$6,000 x 1.34392 = \$8,064

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Module 7 I Liability Recognition and Nonowner Financing 7-32 re Value of an Annuity ad of investing a single amount, we invest a specified amount eachperiod, then we have an annuity. To e, assume that we decide to invest \$2,000 at the end of each year for five years at an 8% annual rate of .To determine the accumulated amount of principal and interest at the end of five years, we refer to Table 4 -~ndix A, which furnishes the future value of a dollar invested at the end of each period. The factor 5.86660 die row for five periods and the column for 8%, and the calculation is as follows: Periodic Payment x Factor \$2,000 x 5.86660 Future Value \$11,733 decide to invest \$1,000 at the end of each six months for five years at an 8% annual rate of return, we would factor for 10 periods at 4%, as follows: Periodic Payment x Factor =
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