298MidtermEquations

# 298MidtermEquations - note not calculated with r p*note FV...

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298 Midterm Equations Simple Interest I = P * r * n I ! total interest P principal r period interest rate n number of periods Compound Interest FV = PV (1 + r p ) n FV future value PV present value r p period interest rate n number of periods Variations r = (FV / PV) -n – 1 PV = FV (1 + r p ) -n n = ln (FV / PV) ln (1 + r) ln natural log Continuous Compounding FV = PV * e (r * n) r = e in – 1 r annual interest rate e exponential function i interest rate n number of years Effective (Annual) Rates (1 + r p ) # = (1 + r a ) r p period rate r a annual rate # periods per year APR [r,m] (1 + r/m) m/k = (1 + r p ) m compounds per year k coupons/payments per year r APR (or ‘nominal’) rate Interest Payments I t = PV (t-1) * r p I t ! interest at year t Annuities {/Bonds} PV = A [ 1 – (1 + r p ) -n ] { + FV(1 + r p ) -n } r p one period before first annuity FV = A [(1 + r p ) n - 1] { + FV(1 + r p ) -n } r p on final annuity date A reoccurring annuity{/coupon}
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Unformatted text preview: note: not calculated with r p *note: FV formula -n refers to years still left (if any) at that point Perpetuity PV = A / r p YTM YTM = r p * k r p periodic rate (not coupon rate) k coupons per year Current Yield (CY) CY = A / P A annuity (/coupon) P price today Bond Selling At… Satisfies This Condition… Discount Coupon Rate < Current Yield < YTM Premium Coupon Rate > Current Yield > YTM Par Value Coupon Rate = Current Yield = YTM (“Coupon Rate” = “Nominal Yield”) Real Rate (Fischer Formula) 1 + r r = (1+ nominal) (1 + inflation) r r real rate Replicating Bonds Time 1 B1 * x + B2 * y = desired \$ Time 2 B1 * x + B2 * y = desired \$\$ x # of B1 coupons y # of B2 coupons...
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