formulas - FNAN 301 Formulas (p. 1 of 5) Value in t periods...

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FNAN 301 Formulas (p. 1 of 5) Value in t periods with simple interest: C 0 × [1 + (simple interest rate per period × t)] = C 0 + (C 0 × simple interest rate per period × t) FV t = C 0 × (1+r) t Financial calculator : In either BEGIN or END mode, FV is the future value in N periods from the reference point (time 0) of a cash flow equal to -PV at the reference point and no other cash flows with a rate of I% per period FV t = C k × (1+r) t-k PV 0 = PV = C t / (1 + r) t = C 0 × [1/ (1+r) t ] Financial calculator : In either BEGIN or END mode, PV is the opposite of the present value as of the reference point (time 0) of a cash flow equal to FV that takes place in N periods from the reference point and no other cash flows with a rate of I% per period PV 0 = PV = C 0 + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] + … + [C t-1 /(1+r) t-1 ] + [C t /(1+r) t ] PV for a fixed perpetuity = [C/(1+r)] + [C/(1+r) 2 ] + [C/(1+r) 3 ] + … = C / r Rate of return for a fixed perpetuity = r = C /PV Cash flow for a fixed perpetuity = C = PV × r PV for a growing perpetuity = C 1 /(1+r) + [C 1 (1+g)]/(1+r) 2 + [C 1 (1+g) 2 ]/(1+r) 3 + … = C 1 / (r – g) Rate of return for a growing perpetuity = r = [C 1 / PV] + g First cash flow for a growing perpetuity = C 1 = PV × (r – g) Growth rate for a growing perpetuity = g = r – [C 1 / PV] C k = C 1 × (1 + g) k – 1 which is the same as C t = C 1 × (1 + g) t – 1 Also, C b = C a × (1 + g) b-a PV for an annuity = [C/(1+r)] + [C/(1+r) 2 ] + … + [C/(1+r) t ] = C × [{1 – 1/(1+r) t } / r ] = C × [(1/r) – 1/{r(1+r) t }] Financial calculator : In END mode, PV is the opposite of the present value as of the reference point (time 0) of a series of N regular cash flows equal to PMT per period where the first regular cash flow takes place 1 period from the reference point, the last cash flow takes place N periods from the reference point, and the rate is I% per period PV for an annuity due = (1+r) × PV for an annuity = C + [C/(1+r)] + [C/(1+r) 2 ] + [C/(1+r) 3 ] + … + [C/(1+r) t-1 ] = (1+r) × C × [{1 – 1/(1+r) t } / r ] = (1+r) × C × [(1/r) – 1/{r(1+r) t }] Financial calculator : In BEGIN mode, PV is the opposite of the present value as of the reference point (time 0) of a series of N regular cash flows equal to PMT per period where the first regular cash flow takes place at the reference point, the last cash flow takes place N-1 periods from the reference point, and the rate is I% per period FV t = [C 0 × (1+r) t ] + [C 1 × (1+r) t-1 ] + [C 2 × (1+r) t-2 ] + … + [C k × (1+r) t-k ] + … + [C t-1 × (1 + r) 1 ] + [C t ] FV for an annuity = [C 1 × (1+r) t-1 ] + [C 2 × (1+r) t-2 ] + … + C t = (1+r) t × C × [{1 – 1/(1+r) t } / r] = C × [{(1+ r) t – 1} / r] = (1+r) t × C × [(1/r) – 1/{r(1+r) t }] Financial calculator : In END mode, FV is the future value in N periods from the reference point (time 0) of a series of N regular cash flows equal to -PMT per period where the first regular cash flow takes place 1 period from
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formulas - FNAN 301 Formulas (p. 1 of 5) Value in t periods...

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