BAC1644
Tutorial
Chapter 5
–
Part 2
12.
For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR /
m
)]
m
–
1
EAR = [1 + (.08 / 4)]
4
–
1
= .0824 or 8.24%
EAR = [1 + (.18 / 12)]
12
–
1
= .1956 or 19.56%
EAR = [1 + (.14 / 365)]
365
–
1
= .1502 or 15.02%
EAR = [1 + (.12 / 2)]
2
–
1
= .1236 or 12.36%
13.
Here we are given the EAR and need to find the APR. Using the equation for discrete compounding:
EAR = [1 + (APR /
m
)]
m
–
1
We can now solve for the APR. Doing so, we get:
APR =
m
[(1 + EAR)
1/
m
–
1]
EAR = .12 = [1 + (APR / 2)]
2
–
1
APR = 2[(1.12)
1/2
–
1]
= 11.66%
EAR = .08 = [1 + (APR / 12)]
12
–
1
APR = 12[(1.08)
1/12
–
1]
= 7.72%
EAR = .13 = [1 + (APR / 52)]
52
–
1
APR = 52[(1.13)
1/52
–
1]
= 12.24%
EAR = .11 = [1 + (APR / 365)]
365
–
1
APR = 365[(1.11)
1/365
–
1]
= 10.44%
19.
The APR is simply the interest rate per period times the number of periods in a year. In this case, the
interest rate is 15 percent per month, and there are 12 months in a year, so we get:
APR = 12(15%)
APR = 180%
To find the EAR, we use the EAR formula:
EAR = [1 + (APR /
m
)]
m
–
1
EAR = (1 + .15)
12
–
1
EAR = 4.3503 or 435.03%
Notice that we didn’t need to divide the APR by the number of compounding periods per year. We
do this division to get the interest rate per period, but in this problem we are already given the
interest rate per period.
20.
We first need to find the annuity payment. We have the PVA, the length of the annuity, and the
interest rate. Using the PVA equation:
PVA =
C
({1 – [1/(1 +
r
)
t
]} /
r
)
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View Full DocumentBAC1644
Tutorial
Chapter 5
–
Part 2
$73,800 = $
C
[1
–
{1 / [1 + (.061/12)]
60
} / (.061/12)]
Solving for the payment, we get:
C
= $73,800 / 51.6014
C
= $1,430.20
To find the EAR, we use the EAR equation:
EAR = [1 + (APR /
m
)]
m
–
1
EAR = [1 + (.061 / 12)]
12
–
1
EAR = .0627 or 6.27%
21.
Here we need to find the length of an annuity. We know the interest rate, the PV, and the payments.
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 Spring '11
 Adams
 Time Value Of Money, Interest, 6.27%, 8.24%, 7.72%, 2,600%

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