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Since your salary grows at 4 percent, you deposit will also grow at 4 percent. We can use the
present value of a
growing perpetuity equation to find the value of your deposits today. Doing so, we find:
PV =
C
{[1/(
r
–
g
)] – [1/(
r
–
g
)] × [(1 +
g
)/(1 +
r
)]
t
}
PV = $2,600{[1/(.11 – .04)] – [1/(.11 – .04)] × [(1 + .04)/(1 + .11)]
40
}
PV = $34,399.45
Now, we can find the future value of this lump sum in 40 years. We find:
FV = PV(1 +
r
)
t
FV = $34,366.45(1 + .11)
40
FV = $2,235,994.31
This is the value of your savings in 40 years.
39.
The relationship between the PVA and the interest rate is:
PVA falls as
r
increases, and PVA rises as
r
decreases
FVA rises as
r
increases, and FVA falls as
r
decreases
The present values of $9,000 per year for 10 years at the various interest rates given are:
PVA@10% = $9,000{[1 – (1/1.10)
15
] / .10} = $68,454.72
PVA@5% = $9,000{[1 – (1/1.05)
15
] / .05} = $93,416.92
PVA@15% = $9,000{[1 – (1/1.15)
15
] / .15} = $52,626.33
40.
Here we are given the FVA, the interest rate, and the amount of the annuity. We need to solve
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This note was uploaded on 07/15/2010 for the course FINANCE 318 taught by Professor Spurlin during the Spring '08 term at LA Tech.
 Spring '08
 spurlin
 Perpetuity

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