Problem Set: Interest Rates
(Solutions Below)
Percentages and Basis Points
1. Express 1% as a decimal and in basis points.
2. Express 0.0025 as a percentage integer and in basis
points.
3. Express 15 basis points as a percentage integer and a
decimal.
Compound Rates
4. If $100 grows to $500 in 5 years, what is the annual
compound rate of interest?
5. If $11.15 grows to $30.34 in 7 years, what is the annual
compound rate of interest?
Holding Period Return
6. If a stock price is $102.78 in June and $120.56 one month
later, what is the holding period return?
7. If a stock price is $45.00 in May and $43.55 one month
later, what is the holding period return?
8. Find the monthly holding period returns, the quarterly
holding period returns, and the annual holding period
return:
Month
December
January
February
March
April
May
Price
$99.76
$101.56
$105.67
$110.55
$102.77
$107.45
Annual Percentage Rate (APR)
9. If a stock price is $103.45 in June and $105.11 one month
later, what is the APR?
10.
If a stock price is $45.00 in May and $43.55 one
month later, what is the APR?
11.
If the APR (based on monthly data) is 15.6%, what is
the EAR?
12.
If the APR (based on quarterly data) is 12.5%, what is
the EAR?
13.
If the EAR is 17.8%, what is the APR (based on weekly
data)?
Effective Annual Return (EAR)
14.
If a stock price is $102.78 in June and $120.56 one
month later, what is the EAR?
15.
If a stock price is $45.00 in May and $43.55 one
month later, what is the EAR?
16.
Find the monthly EAR and the quarterly EAR (this is
the same data as about, so you can begin with those
results:
Month
December
January
February
March
April
May
Price
$99.76
$101.56
$105.67
$110.55
$102.77
$107.45
Annual and Non-Annual Rate Conversions
17.
If the monthly return is 2.1%, find the daily (365 days
in a year), weekly, quarterly, semi-annual and annual
returns.
18.
If the weekly return is 0.6%, find the daily (365 days in
a year), monthly, quarterly, semi-annual and annual
returns.
19.
If the annual return is 10.1%, find the daily (365 days
in a year), weekly, monthly, quarterly, and semi-annual
returns.
20.
If the daily return is 5 basis points (365 days in a year),
find the weekly, monthly, quarterly, semi-annual, and
annual returns.
Continuous Time Rates
21.
If the annual return is 2.1%, find the continuous time
return.
22.
If the weekly return is 0.6%, find the continuous time
return.
23.
If the quarterly return is 3.4%, find the continuous time
return.
24.
If the monthly return is 1.1%, find the continuous time
return.
25.
If the daily return is 4 basis points, find the continuous
time return.
26.
If the continuous time return is 10%, find the annual
return.
27.
If the continuous time return is 11.8%, find the
monthly return.
28.
If the continuous time return is 9.1%, find the weekly
return.
29.
If the continuous time return is 4.5%, find the quarterly
return.
30.
If the continuous time return is 11.2%, find the semiannual return.
Arithmetic Average versus Geometric Average
31.
Find the arithmetic and geometric averages for the
following series:
10.1%
11.3%
14.0%
12.3%
15.7%
10.4%
32.
Find the arithmetic and geometric averages for the
following series:
0.163
0.123
0.130
0.141
0.120
0.091
Solutions
Percentages and Basis Points
1. Express 1% as a decimal and in basis points.
1% = 0.01 = 100 basis points
2. Express 0.0025 as a percentage integer and in basis
points.
0.0025 = 0.25% = 25 basis points
3. Express 15 basis points as a percentage integer and a
decimal.
15 basis points = 0.15% = 0.0015
Compound Rates
4. If $100 grows to $500 in 5 years, what is the annual
compound rate of interest?
P/Y = 1; N = 5; I/Y = 37.97; PV = -100; PMT = 0; FV = 500
5. If $11.15 grows to $30.34 in 7 years, what is the annual
compound rate of interest?
P/Y = 1; N = 7; I/Y = 15.37; PV = 11.15; PMT = 0; FV = 30.34
Holding Period Return
6. If a stock price is $102.78 in June and $120.56 one month
later, what is the holding period return?
HPR 
120.56  102.78
= 17.30%
102.78
P/Y = 1; N = 1; I/Y = 17.30; PV = -120.56; PMT = 0; FV =
102.78
7. If a stock price is $45.00 in May and $43.55 one month
later, what is the holding period return?
HPR 
43.55  45.00
 -3.22%
45.00
P/Y = 1; N = 1; I/Y = -3.22; PV = -45.00; PMT = 0; FV = 43.55
8. Find the monthly holding period returns:
Month
December
January
February
March
April
May
Price
$99.76
$101.56
$105.67
$110.55
$102.77
$107.45
101.56  99.76
 1.80%
99.76
105.67  101.56
HPRFeb 
 4.05%
101.56
110.55  105.67
HPRMar 
 4.62%
105.67
102.77  110.55
HPRApr 
 -7.04%
110.55
107.45  102.77
HPRMay 
 4.55%
102.77
HPRJan 
Annual Percentage Rate (APR)
9. If a stock price is $103.45 in June and $105.11 one month
later, what is the APR?
105.11  103.45
 1.60%
103.45
APR  1.60  12  19.26%
HPR 
10.
If a stock price is $45.00 in May and $43.55 one
month later, what is the APR?
43.55  45.00
 3.22%
45.00
APR  3.22  12  -38.67%
HPR 
11.
If the APR (based on monthly data) is 15.6%, what is
the EAR?
12
0.156 

EAR   1 
 1  16.77%
12 

NOTE: Your calculator may have a function to convert
APR to EAR.
12.
If the APR (based on quarterly data) is 12.5%, what is
the EAR?
4
0.125 

EAR   1 
 1  13.10%
4 

13.
If the EAR is 17.8%, what is the APR (based on weekly
data)?
52
APR 

0.178   1 
1
52 

52
APR 

1+0.178   1 
52 

1
APR
1.178  52  1 
52
1
APR
1.178  52  1 
52
1


52  1.178  52  1  APR  16.41%


NOTE: Your calculator may have a function to convert
EAR to APR.
Effective Annual Return (EAR)
14.
If a stock price is $102.78 in June and $120.56 one
month later, what is the EAR?
EAR  1.1730   1  578.54%
12
15.
If a stock price is $45.00 in May and $43.55 one
month later, what is the EAR?
EAR  1  0.0322   1  -32.48%
12
16.
Find the monthly EAR (this is the same data as about,
so you can begin with those results):
Month
December
January
February
March
April
May
Price
$99.76
$101.56
$105.67
$110.55
$102.77
$107.45
EARJan  1.018   1  23.94%
12
EARFeb  1.0405   1  60.97%
12
EARMar  1.0462   1  71.90%
12
EARApr  1  0.0704   1  -58.36%
12
EARMay  1.0455   1  70.56%
12
Annual and Non-Annual Rate Conversions
17.
If the monthly return is 2.1%, find the daily (365 days
in a year), weekly, quarterly, semi-annual and annual
returns.
EAR  1.021  1  28.32%
12
1
rdaily  1.2832  365  1  0.07%
1
rweekly  1.2832  52  1  0.48%
1
rquarterly  1.2832  4  1  6.43%
1
rsemi-annually  1.2832  2  1  13.28%
18.
If the weekly return is 0.6%, find the daily (365 days in
a year), monthly, quarterly, semi-annual and annual
returns.
EAR  1.006   1  36.49%
52
1
rdaily  1.3649  365  1  0.09%
1
rmonthly  1.3649 12  1  2.63%
1
rquarterly  1.3649  4  1  8.09%
1
rsemi-annually  1.3649  2  1  16.29%
19.
If the annual return is 10.1%, find the daily (365 days
in a year), weekly, monthly, quarterly, and semi-annual
returns.
1
rdaily  1.101 365  1  0.03%
1
rweekly  1.101 52  1  0.19%
1
rmonthly  1.10112  1  0.81%
1
rquarterly  1.101 4  1  2.43%
1
rsemi-annually  1.101 2  1  4.93%
20.
If the daily return is 5 basis points (365 days in a year),
find the weekly, monthly, quarterly, semi-annual, and
annual returns.
EAR  1.0005 
365
 1  20.02%
1
rweekly  1.2002  52  1  0.35%
1
rmonthly  1.2002 12  1  1.53%
1
rquarterly  1.2002  4  1  4.67%
1
rsemi-annually  1.2002  2  1  9.55%
Continuous Time
NOTE: When converting a non-annual rate to a
continuous time rate, first find the EAR, then the
continuous time rate.
21.
1. If the annual return is 2.1%, find the continuous
time return.
rc  ln 1.021
rc  2.08%
22.
2. If the weekly return is 0.6%, find the continuous
time return.
EAR  1.006   1  36.49%
52
rc  ln 1.3649 
rc  31.11%
23.
3. If the quarterly return is 3.4%, find the continuous
time return.
EAR  1.034   1  14.31%
4
rc  ln 1.1431
rc  13.37%
24.
4. If the monthly return is 1.1%, find the continuous
time return.
EAR  1.011  1  14.03%
12
rc  ln 1.1403 
rc  13.13%
25.
5. If the daily return is 4 basis points, find the
continuous time return.
EAR  1.0004 
365
 1  15.72%
rc  ln 1.1572 
rc  14.60%
26.
6. If the continuous time return is 10%, find the annual
return.
EAR  e0.10  1
EAR  10.52%
27.
7. If the continuous time return is 11.8%, find the
monthly return.
EAR  e0.118  1  12.51%
1
rmonthly  1.125112  1
rmonthly  0.99%
28.
8. If the continuous time return is 9.1%, find the
weekly return.
EAR  e0.091  1  9.53%
1
rweekly  1.0943  52  1
rweekly  0.17%
29.
9. If the continuous time return is 4.5%, find the
quarterly return.
EAR  e0.045  1  4.60%
1
rquarterly  1.0460  4  1
rquarterly  1.13%
30.
10. If the continuous time return is 11.2%, find the
semi-annual return.
EAR  e0.112  1  11.85%
1
rsemi annually  1.1185  2  1
rsemi annually  5.76%
Arithmetic Average versus Geometric Average
31.
1. Find the arithmetic and geometric averages for
the following series:
10.1%
11.3%
14.0%
12.3%
15.7%
10.4%
a 
0.101  0.113  0.140  0.123  0.157  0.104
 12.30%
6
g  6 1.101 1.113  1.140  1.123  1.157  1.104  1  12.28%
32.
2. Find the arithmetic and geometric averages for
the following series:
0.163
0.123
0.130
0.141
0.120
0.091
a 
0.163  0.123  0.130  0.141  0.120  0.091
 12.80%
6
g  6 1.163  1.123  1.130  1.141 1.120  1.091  1  12.78%