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Using the EAR and the number of years to find the FV, we get:
FV in one year = $1(1.1498)
1
= $1.15
FV in two years = $1(1.1498)
2
= $1.32
Either method is correct and acceptable. We have simply made sure that the interest
compounding period is the same
as the number of periods we use to calculate the FV.
34.
Here we are finding the annuity payment necessary to achieve the same FV. The interest rate
given is a 12 percent
APR, with monthly deposits. We must make sure to use the number of months in the equation.
So, using the FVA
equation:
Starting today:
FVA =
C
[{[1 + (.12/12) ]
480
– 1} / (.12/12)]
C
= $1,000,000 / 11,764.77 = $85.00
Starting in 10 years:
FVA =
C
[{[1 + (.12/12) ]
360
– 1} / (.12/12)]
C
= $1,000,000 / 3,494.96 = $286.13
Starting in 20 years:
FVA =
C
[{[1 + (.12/12) ]
240
– 1} / (.12/12)]
C
= $1,000,000 / 989.255 = $1,010.86
Notice that a deposit for half the length of time, i.e. 20 years versus 40 years, does not mean that
the annuity payment
is doubled. In this example, by reducing the savings period by onehalf, the deposit necessary to
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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
 Compounding, Interest

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