CHAPTER 7
B-133
35.
To answer this question, we need to find the monthly interest rate, which is the APR divided by 12.
We also must be careful to use the real interest rate. The Fisher equation uses the effective annual
rate, so, the real effective annual interest rates, and the monthly interest rates for each account are:
Stock account:
(1 +
R
) = (1 +
r
)(1 +
h
)
1 + .11 = (1 +
r
)(1 + .04)
r
= .0673 or 6.73%
APR =
m
[(1 + EAR)
1/
m
– 1]
APR = 12[(1 + .0673)
1/12
– 1]
APR = .0653 or 6.53%
Monthly rate = APR / 12
Monthly rate = .0653 / 12
Monthly rate = .0054 or 0.54%
Bond account:
(1 +
R
) = (1 +
r
)(1 +
h
)
1 + .07 = (1 +
r
)(1 + .04)
r
= .0288 or 2.88%
APR =
m
[(1 + EAR)
1/
m
– 1]
APR = 12[(1 + .0288)
1/12
– 1]
APR = .0285 or 2.85%
Monthly rate = APR / 12
Monthly rate = .0285 / 12
Monthly rate = .0024 or 0.24%
Now we can find the future value of the retirement account in real terms. The future value of each
account will be:
Stock account:
FVA =
C
{(1 +
r
)
t
– 1] /
r
}
FVA = $900{[(1 + .0054)
360
– 1] / .0054]}
FVA = $1,001,704.05
Bond account:
FVA =
C
{(1 +
r
)
t
– 1] /
r
}
FVA = $450{[(1 + .0024)
360
– 1] / .0024]}
FVA = $255,475.17
The total future value of the retirement account will be the sum of the two accounts, or:
Account value = $1,001,704.05 + 255,475.17
Account value = $1,257,179.22

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