Problem Set: Interest Rates, Amortization,
Inflation, and Yield Curve
(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.
Amortization
21.
Complete the amortization table for a three year
loan of $2,000 at 9%.
Year Beginning
Total
Interest
Principal
End
Balance
Payment
Payment
Payment
Balance
1
2
3
22.
Complete the amortization table for a three year
loan of $5,000 at 4%.
Beginning
Total
Year Balance Payment
1
2
3
Interest
Payment
Principal
Payment
End
Balance
Real versus Nominal Cash Flows
23.
Convert the following series of nominal cash flows to
real cash flows (i = 5.1%):
1
100.56
2
20.56
3
313.67
4
-200.16
5
450.66
24.
Convert the following series of real cash flows to
nominal cash flows (i = 6.2%):
1
25.67
2
13.45
3
-45.31
4
56.87
5
24.50
25.
If a nominal cash flow in year 5 is $234.71 and the
corresponding real cash flow is $215.67, what is the rate of
inflation?
Real versus Nominal Rates of Interest
26.
If the real interest rate is 5.3% and inflation is 4%, find
the nominal rate of interest.
27.
If the nominal interest rate is 12.4% and inflation is
7.8%, find the real rate of interest.
28.
If the nominal interest rate is 10.1% and the real
interest rate is 8.7%, find the inflation rate.
Yield Curve
29.
Calculate the implied future interests rate for the
following yield curve.
Year
1
2
3
4
Rate
7.80
7.50
7.30
7.10
30.
Calculate the implied future interests rate for the
following yield curve.
Year
1
2
3
4
Rate
6.50
6.70
6.90
7.20
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 

 1  16.77%
EAR   1 
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 

 1  13.10%
EAR   1 
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%
Amortization
21.
Complete the amortization table for a three year
loan of $2,000 at 9%.
Year
1
2
3
Beginning
Total
Balance Payment
$2,000.00
$790.11
$1,389.89
$790.11
$724.87
$790.11
Interest
Payment
$180.00
$125.09
$65.24
Principal
Payment
$610.11
$665.02
$724.87
End
Balance
$1,389.89
$724.87
$0.00
Total Payment:
P/Y = 1; N = 3; I/Y = 9; PV = -2,000; PMT = $790.11; FV = 0
Steps:
a)
b)
c)
d)
e)
Beginning Balance (Year 1) = Loan amount = $2,000
Interest Payment = Interest Rate x Beginning Balance
Principal Payment = Total Payment – Interest Payment
End Balance = Beginning Balance – Principal Payment
Beginning Balance = End Balance (previous year)
22.
Complete the amortization table for a three year
loan of $5,000 at 4%.
Year
1
2
3
Beginning
Total
Balance Payment
$5,000.00 $1,801.74
$3,398.26 $1,801.74
$1,732.44 $1,801.74
Interest
Payment
$200.00
$135.93
$69.30
Principal
Payment
$1,601.74
$1,665.81
$1,732.44
End
Balance
$3,398.26
$1,732.44
$0.00
Total Payment:
P/Y = 1; N = 3; I/Y = 4; PV = -5,000; PMT = $1,801.74; FV = 0
Steps (as above)
Real versus Nominal Cash Flows
23.
Convert the following series of nominal cash flows to
real cash flows (i = 5.1%):
1
100.56
2
20.56
3
313.67
4
-200.16
5
450.66
P/Y = 1; N = 1; I/Y = 5.1; PV = $95.68; PMT = 0; FV = -100.56
P/Y = 1; N = 2; I/Y = 5.1; PV = -$18.61; PMT = 0; FV = -20.56
P/Y = 1; N = 3; I/Y = 5.1; PV = $270.19; PMT = 0; FV = -313.67
P/Y = 1; N = 4; I/Y = 5.1; PV = -$164.05; PMT = 0; FV = 200.16
P/Y = 1; N = 5; I/Y = 5.1; PV = $351.43; PMT = 0; FV = 450.66
NOTE: Converting from nominal cash flows to real cash
flows is the equivalent of discounting by the rate of
inflation.
24.
Convert the following series of real cash flows to
nominal cash flows (i = 6.2%):
1
25.67
2
13.45
3
-45.31
4
56.87
5
24.50
P/Y = 1; N = 1; I/Y = 6.2; PV = -25.67; PMT = 0; FV = $27.26
P/Y = 1; N = 2; I/Y = 6.2; PV = -13.45; PMT = 0; FV = $15.17
P/Y = 1; N = 3; I/Y = 6.2; PV = 45.31; PMT = 0; FV = -$54.27
P/Y = 1; N = 4; I/Y = 6.2; PV = -56.87; PMT = 0; FV = $72.34
P/Y = 1; N = 5; I/Y = 6.2; PV = -24.50; PMT = 0; FV = $33.10
NOTE: Converting from real cash flows to nominal cash
flows is the equivalent of compounding by the rate of
inflation.
25.
If a nominal cash flow in year 5 is $234.71 and the
corresponding real cash flow is $215.67, what is the rate of
inflation?
234.71  215.67 1  i 
5
234.71
5
 1  i 
215.67
1
 234.71  5
 215.67   1  i


1
 234.71  5
 215.67   1  i  1.71%


Real versus Nominal Rates of Interest
26.
If the real interest rate is 5.3% and inflation is 4%, find
the nominal rate of interest.
1  rn  1.053 1.04 
rn  1.053 1.04   1
rn  9.51%
27.
If the nominal interest rate is 12.4% and inflation is
7.8%, find the real rate of interest.
1.124
1.078
1.124
rr 
1
1.078
rr  4.27%
1  rr 
28.
If the nominal interest rate is 10.1% and the real
interest rate is 8.7%, find the inflation rate.
1.101  1.087 1  i 
1.101
 1 i
1.087
1.101
1 i
1.087
i  1.29%
Yield Curve
29.
Calculate the implied future interests rate for the
following yield curve.
Year
1
2
3
4
Rate
7.80
7.50
7.30
7.10
2
%
0
2
.
7
%
0
9
.
6
%
0
5
.
6
1.0750   1 
f2 
1.0780 
3
1.0730 

f3 
1
2
1.0750 
4
1.0710 

f4 
1
3
1.0730


30.
Calculate the implied future interests rate for the
following yield curve.
Year
1
2
3
4
Rate
6.50
6.70
6.90
7.20
2
%
0
9
.
6
%
0
3
.
7
%
1
1
.
8
1.0670   1 
f2 
1.0650 
3
1.0690 

f3 
1
2
1.0670 
4
1.0720 

f4 
1
3
1.0690 