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 Price
December $99.76
January $101.56
February $105.67
March $110.55
April $102.77
May $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 Price
December $99.76
January $101.56
February $105.67
March $110.55
April $102.77
May $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 semi-
annual 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?
120.56 102.78
HPR = 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?
43.55 45.00
HPR -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 Price
December $99.76
January $101.56
February $105.67
March $110.55
April $102.77
May $107.45
101.56 99.76
HPRJan 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
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
HPR 1.60%
103.45
APR 1.60 12 19.26%
10. If a stock price is $45.00 in May and $43.55 one
month later, what is the APR?
43.55 45.00
HPR 3.22%
45.00
APR 3.22 12 -38.67%
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 Price
December $99.76
January $101.56
February $105.67
March $110.55
April $102.77
May $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 1.10112 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 e 0.10 1
EAR 10.52%
27. 7. If the continuous time return is 11.8%, find the
monthly return.
EAR e 0.118 1 12.51%
1
rmonthly 1.125112 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 e 0.045 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 e 0.112 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%
0.101 0.113 0.140 0.123 0.157 0.104
a 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
0.163 0.123 0.130 0.141 0.120 0.091
a 12.80%
6
g 6 1.163 1.123 1.130 1.141 1.120 1.091 1 12.78%