By John Mueller

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1. Nominal and Effective Interest Spot rates are interest rates based on the yield from pure discount bonds (The one year Treasury bond is usual for the one year rate). We will cover bonds and bond yields later on in this chapter. For now we will take it that the spot rate is calculated from the yield on a bond contract. Spot rates are quoted on a period (time related) basis as the 1 year, 2 year or n-year spot rate. 1) Where Pn is the current market valuation of a pure discount bond with n years and has a face value of Vn .

Future value calculations can be based on a so-called riskless basis with known interest rates, or can be based on varying interest and changing risk environments. 1) This formula can be generalised for a series of varying amounts At as: PV = n At i i=1 1 + r This formula calculates the series of equal payments (in arrears) over a given time frame (n). Where, i is the time period and r is the interest rate. 1. Compounding Cashflows The class PresentValue contains methods to calculate present values of a series of cashflows.

The spot rate is in . In the absence of pure longer term Treasury bonds, the n-year spot rate is calculated by taking the one year calculation and using coupon bearing bond prices. 2) This process can continue in an iterative fashion to provide n-year spot rates, based on n-year coupons. When spot rates are known the future values of investments or debt can be discounted. For an overview see Adams et al (1993). Interest rates are time dependent. A rate of 10% per annum is the effective rate over 12 months, whereas the rate of 10% over 3 months is the effective rate for a quarter year and not the effective rate per annum.

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Visual C++ 6 from the Ground Up by John Mueller
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