Fin 300 Exam 2 Equations

Ordinary annuity (Future Value)

FV_t = C * [((1 + r)^t - 1) / r]

Ordinary annuity (Present Value)

PV_0 = C * [(1 - (1 + r)^-t) / r]

Ordinary annuity (Solve for t given FV)

t = [ln(r * FV / C + 1)] / ln(1 + r)

Ordinary annuity (Solve for t given PV)

t = [ln(C / (C - r * PV))] / ln(1 + r)

Ordinary annuity (Solve for C given FV)

C = (FV_t * r) / ((1 + r)^t - 1)

Ordinary annuity (Solve for C given PV)

C = (PV_0 * r) / (1 - (1 + r)^-t)

Annuity due (Future Value)

FV_t = C * [((1 + r)^t - 1) / r] * (1 + r)

Annuity due (Present Value)

PVdue = PVordinary * (1 + r)

Annuity due (Payment)

Paymentdue = Paymentordinary / (1 + r)

Growing annuity (Future Value)

FVt = C1 * [((1 + r)^t - (1 + g)^t) / (r - g)]

Growing annuity (Present Value)

PV0 = C1 * [(1 - ((1 + g) / (1 + r))^t) / (r - g)]

Level perpetuity (Present Value)

PV0 = C1 / r

Growing perpetuity (Present Value)

PV0 = C1 / (r - g)

Bond Price (Present Value)

PV = C * [(1 - (1 + r)^-t) / r] + FV * (1 + r)^-t

Yield to Maturity (APR)

YTM = r * m

Periodic Rate

r = YTM / m

Current Yield

Current Yield = Annual Coupons / Current Market Price

European-style Bond (YTM Components)

YTM = Current Yield + Capital Gains Yield

American-style Bond (YTM Components)

YTM ≈ Current Yield + Capital Gains Yield

Dollar return

Dollar Return = P1 - P0 + CF_1

Total return

Total Return = (P1 - P0) / P0 + CF1 / P_0

Geometric return

Geometric Return = (FV / PV)^(1/t) - 1

Annual percentage rate (APR)

APR = r * m

Annual percentage yield (Form I)

APY = (1 + APR / m)^m - 1

Annual percentage yield (Form II)

APY = (1 + r)^m - 1

Continuous compounding (APY)

APY = e^APR - 1

Continuous compounding (Future Value)

FV = PV * e^(APR * t)

Continuous compounding (Present Value)

PV = FV * e^-(APR * t)

Continuous compounding (Solve for APR)

APR = ln(FV / PV) / t

Continuous compounding (Solve for t)

t = ln(FV / PV) / APR