Chapter 4 Understanding Money and Its Management
Nominal and Effective Interest Rates
4.1
• Nominal interest rate:
4.2
(a) Monthly interest rate:
17.85% 12 1.4875%i= ÷=
4.3 Assuming weekly compounding:
4.4
• Interest rate per week
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4.5 The effective annual interest rate :
4.6 Interest rate per week:
4.7 The effective annual interest rate :
4.8
24-month lease plan with 40,000 miles over 2 years:
4.9 The three options :
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4.10
4.11
Bank A:
365
0.05
1 1 5.127%
365
a
i
= + −=
Compounding More Frequent than Annually
4.12
4.13
4.14
(0.09 5)
$5,000
$7,841.56
rN
F Pe e
×
= =
=
4.15
4.16
(a) Nominal interest rate:
2.32% 12 27.84%r= ×=
(b) Effective annual interest rate:
4.17
8
0.08
$15, 000(1 ) $15, 000( / , 2%,8)
4
$17,575
F FP= +=
=
4.18
4.19
(a)
24
0.082
$9,545(1 ) $9,545( / , 4.1%, 24)
2
$25,037.64
F FP=+=
=
(b)
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(c)
96
0.09
$42,800(1 ) $42,000( / ,0.75%,96)
12
$87,693.83
F FP= +=
=
4.20
(a) Quarterly interest rate = 2.25%
(c)
0.09
3
ln(3) 0.09
12.20 years
N
e
N
N
=
=
=
4.21
(a) Quarterly effective interest rate = 1.5%
4.22
$7,500( / , 0.669%, 60) $551, 479F FA= =
4.23
(a) Quarterly effective interest rate = 2.25%
4.24 (d)
4.25
0.086/4
1 2.1733%
a
ie= −=
Effective interest rate per
payment period
i = (1 + 0.01)3 – 1
= 3.03%
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4.26
(a) Monthly effective interest rate = 0.74444%
4.27
(b)
4.28
0.0225 1 2.2755%ie= −=
4.29
4.30
Effective interest rate per quarter =
e
0.0688/ 4
−1=1.7349%
4.31
(a)
$20,000( / , 4%,10) $240,122F FA= =
4.33
(a)
A=$45,000( A/F,3.725%,20) =$
1,554.80
4.34
4.35
$25,000 $489.15( / , ,60)P Ai=
4.36
$30,000 $500( / , , 20)
F Ai
=
4.37
$15, 000 $409.61( / , , 42)
P Ai
=
4.38
4.39
(a)
$5, 000( / , 4.5%, 24) $72, 477P PA= =
4.40
• Equivalent future worth of the receipts:
4.41
• The balance just before the transfer:
F
9
=$22,000(F/P,0.5%,108) +$16,000(F/P,0.5%,72)
4.42
Establish the cash flow equivalence at the end of 25 years. Let’s define A as the
4.43
• Monthly installment amount:
4.44
$225,000 $5,000( / ,0.75%, )
PA N
=
4.45
$20,000 $650.52( / , ,36)
P A i
=
4.46
Given
%6=r
per year compounded monthly, the effective annual rate is
6.168%.
Now consider the four options:
1. Renew every three-month at $45 for two years.
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4.47
To find the amount of quarterly deposit (A), we establish the following
4.48
Setting the equivalence relationship at the end of 20 years gives
4.49
Given
5% 0.417% per month
i= =
4.50
First compute the equivalent present worth of the energy cost savings during the
first operating cycle:
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Continuous Payments with Continuous Compounding
4.51
Given
i=10%, N=10 years, and A=$95,000 ×365 =$34,675,000
• Daily payment with daily compounding:
4.52
$70 $70 $70 $80 $80 $80
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4.53
Given
9%, $25,000, 2, 7,
se
r A NN= = = =
7
4.54
$500,000
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Changing Interest Rates
4.55
4.56
Given
%6
1=r
compounded quarterly,
%10
2
=r
compounded quarterly, and
%8
3=r
compounded quarterly, indicating that
%5.1
1
=i
per quarter,
%5.2
2=i
per quarter, and
%2
3=i
per quarter.
(a) Find P:
(b) Find F:
(c) Find A, starting at 1 and ending at 5:
4.57
(a)
)12%,5.0,/)(12%,75.0,/(300$)12%,5.0,/(300$
+=
FPFPFPP
(b)
4.58
Since payments occur annually, you may compute the effective annual interest
rate for each year.
4.59
0.06 0.08
12
1 6.18%, 1 8.33%ie ie= −= = −=
Amortized Loans
4.60
Loan repayment schedule for the selected 6 payments:
End of
month
Interest Payment
Principal
Payment
Remaining
Balance
0
$0.00
$0.00
$20,000.00
1
$100.00
$508.44
$19,491.56
2
$510.98
$18,980.58
$3.03
$605.41
4.61
(a)
(i)
)24%,75.0,/(000,10$ PA
(b)
4.62
Given information:
9.45% / 365 0.0259% per dayi= =
, N = 36 months.
4.63
A=$20,200( A/P,(9.2 / 12)%,48)=$504.59
(b)
Using the dealer’s financing,
4.64
Given Data: P = $25,000, r = 9% compounded monthly, N = 36 month, and
i = 0.75% per month.
• Required monthly payment:
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4.65
Given Data: P = $250,000 – $50,000 = $200,000.
• Option 1:
4.66
• The monthly payment to the bank: Deferring the loan payment for 6 months is
equivalent to borrowing
• The remaining balance after making the 16th payment:
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4.67
(b) Remaining balance after the 59th payment:
4.68
9%
$400,000( / , ,180) $4,057.07
12
A AP= =
• Total payments over the first 5 years (60 months)
4.69
The amount to finance = $300,000 – $45,000 = $255,000
4.70
Given Data: purchase price = $150,000, down payment (sunk equity) = $30,000,
interest rate = 0.75% per month, N = 360 months,