TABLE OF FORMULAS1. CIRCLE(x − h)2+(y − k)2= r22. PARABOLAy − k = a(x − h)2The graph of the functiony = f (x)=ax2+ bx + c (a 6=0)is a parabola with vertex at−b2a,c−b24a.3. COMPOUND INTEREST FORMULA. A principal P , earning interest com-pounded k times a year for n yearsatanannualrater, will grow to the future valueFV according to the formulaFV = P (1 + i)knwhere i =rkis the periodic interest rate.4. EFFECTIVE RATE OF INTEREST. The effective rate of interest R for anaccount paying a nominal rate r, compounded k times per year, isR =(1+i)k− 1where i is the periodic rate, i =rk.5. PRESENT VALUE. The present value PV that must be deposited now to providea future value, FV, n years from now is given by the formulaPV = FV(1 + i)−knwhere interest is compounded k times per year at an annual rate r (i is the periodicrate,rk).56. FUTURE VALUE OF AN ANNUITY. The future value FV of an ordinaryannuity with deposits of P dollars made regularly k times each year for n years, withinterest compounded k times per year at an annual rate r,isFV =P [(1 + i)kn− 1]iwhere i is the periodic rate, i =rk.7. SINKING FUND PAYMENT. For an annuity to provide a future value FV,regular deposits P are made k times per year for n years, with interest compoundedk times per year at an annual rate r. The payment P is given byP =FVi(1 + i)kn− 1where i is the periodic rate, i =rk.8. PRESENT VALUE OF AN ANNUITY. The present value PV of an annuitywith payments of P dollars made k times per year for n years, with interest com-pounded k times per year at an annual rate r,isPV =P [1 − (1 + i)−kn]iwhere i is the periodic rate, i =rk.9. INSTALLMENT PAYMENTS. The periodic payment P required to repay anamount A is given byP =Ai1 − (1 + i)−knwherer is the annual rate,k is the frequency of compounding (usually monthly),i is the periodic rate, i =rk,andn is the term of the loan in
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