UGBA 103 – Spring 2011
Solution to Problem Set #2
51.
Your bank is offering you an account that will pay 20% interest in total for a twoyear deposit.
Determine the equivalent discount rate for a period length of
a.
Six months.
b.
One year.
c.
One month.
a.
Since 6 months is
61
24
4
of 2 years, using our rule
1
4
1 0.2
1.0466
So the equivalent 6 month rate is 4.66%.
b.
Since one year is half of 2 years
1
2
1.2
1.0954
So the equivalent 1 year rate is 9.54%.
c.
Since one month is
1
24
of 2 years, using our rule
1
24
1 0.2
1.00763
So the equivalent 1 month rate is 0.763%.
54.
You have found three investment choices for a oneyear deposit: 10% APR compounded monthly,
10% APR compounded annually, and 9% APR compounded daily. Compute the EAR for each
investment choice. (Assume that there are 365 days in the year.)
For a $1 invested in an account with 10% APR with monthly compounding you will have
12
0.1
1
$1.10471
12
So the EAR is 10.471%.
For a $1 invested in an account with 10% APR with annual compounding you will have
1 0.1
$1.10
So the EAR is 10%.
For a $1 invested in an account with 9% APR with daily compounding you will have
365
0.09
1
1.09416
365
So the EAR is 9.416%.
56.
Your bank account pays interest with an EAR of 5%. What is the APR quote for this account based
on semiannual compounding? What is the APR with monthly compounding?
Using the formula for converting from an EAR to an APR quote
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APR
1
1.05
k
Solving for the APR
1
k
APR
1.05
1 k
With annual payments k = 1, so APR = 5%
With semiannual payments k = 2, so APR = 4.939%
With monthly payments k = 12, so APR = 4.889%
59.
Suppose you invest $100 in a bank account, and five years later it has grown to $134.39.
a.
What APR did you receive, if the interest was compounded semiannually?
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 Spring '07
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 Opportunity Cost, Net Present Value

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