[email protected] yrs: PVA = $5,300{[1 – (1/1.07)
75
] / .07} = $75,240.70
To find the PV of a perpetuity, we use the equation:
PV =
C
/
r
PV = $5,300 / .07 = $75,714.29
Notice that as the length of the annuity payments increases, the present value of the annuity
approaches the present
value of the perpetuity. The present value of the 75 year annuity and the present value of the
perpetuity imply that the
value today of all perpetuity payments beyond 75 years is only $473.59.
5.
Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the
annuity payment.
Using the PVA equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
PVA = $34,000 = $
C
{[1 – (1/1.0765)
15
] / .0765}
We can now solve this equation for the annuity payment. Doing so, we get:
C
= $34,000 / 8.74548 = $3,887.72
6.
To find the PVA, we use the equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
PVA = $73,000{[1 – (1/1.085)
8
] / .085} = $411,660.36
7.
Here we need to find the FVA. The equation to find the FVA is:
FVA =
C
{[(1 +
r)
t
– 1] /
r
}
FVA for 20 years = $4,000[(1.112
20
– 1) / .112] = $262,781.16
FVA for 40 years = $4,000[(1.112
40
– 1) / .112] = $2,459,072.63
Notice that because of exponential growth, doubling the number of periods does not merely
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 Spring '08
 spurlin
 Time Value Of Money, Annuity, Perpetuity, FVA.

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