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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)
tk
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
t1
/(1+r)
t1
] + [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)
ba
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)
t1
]
= (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 N1 periods from the reference point, and the rate is I% per period
FV
t
= [C
0
× (1+r)
t
] + [C
1
× (1+r)
t1
] + [C
2
× (1+r)
t2
] + … + [C
k
× (1+r)
tk
] + … + [C
t1
× (1 + r)
1
] + [C
t
]
FV for an annuity = [C
1
× (1+r)
t1
] + [C
2
× (1+r)
t2
] + … + 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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 Fall '08
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