Discussion response, use the corresponding powerpoint to help answer the chapter questions.
Chapter 10: What steps are used to calculate the average daily balance. Many credit cards charge 18%-24% annual interest. Do you think this is fair? Do you think this is a justifiable rate? Should rates be lower for certain age groups or individuals or for different types of credit cards or for different income levels and if so why or why not?
Chapter 19: Explain the difference between future value and present value. Why is future value a good thing to calculate? Explain the difference between simple interest and compound interest
Because learning changes everything.®
Chapter 19
Compound Interest and Present Value
Math for Business and Finance: an Algebraic
Approach, 3rd Edition
Jeffrey Slater
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.
Learning Unit Objectives
LU 19-1: Compound Interest (Future Value) The Big Picture.
1. Compare simple interest with compound interest.
2. Calculate the compound amount and interest manually, by table look
up, using algebraic formulas and with financial calculator.
3. Explain and compute the effective rate (APY).
LU 19-2: Present Value The Big Picture.
1. Compare present value (PV) with compound interest (FV).
2. Compute present value by table look up using algebraic formulas and
with financial calculator.
3. Check the present value answer by compounding.
© McGraw Hill
2
FV = $108.84 Future value
n = 4 (4 years × 1 compounding period per year)
i = 8% (8% divided by 1 compounding period)
PV =
© McGraw Hill
$108.84
( 1+ 0.08)
4
= $80.00
Present value
29
Calculating Present Value
using excel
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© McGraw Hill
19-30
Comparing Compound Interest (FV)
with Present Value (PV)
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© McGraw Hill
19-31
Comparing compound interest (fv)
with Present value (pv)
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© McGraw Hill
19-32
Textbook Problem 19-11
Problem Statement:
Lynn Ally, owner of a local Subway shop, loaned $40,000 to
Pete Hall to help him open a Subway franchise. Pete plans to
repay Lynn at the end of 8 years with 6% interest
compounded semiannually. How much will Lynn receive at
the end of 8 years? LU 19-1(2)
Solution:
6%
8 years ? 2 = 16 periods
=3%
2
$ 40000(1 + .03)16 = $ 40000 ?1.60471= $64188.26
© McGraw Hill
Future value
33
Problem 19-11
Lynn Ally, owner of a local Subway shop, loaned $40,000 to Pete Hall to help him
open a Subway franchise. Pete plans to repay Lynn at the end of 8 years with 6%
interest compounded semiannually. How much will Lynn receive at the end of 8
years? LU 19-1(2)
Solution:
8 years × 2 = 16 periods
6% = 3%
2
$40,000 × (1 = .03)16 = $64,188.26
Step 1: Input 16 and then press N.
Step 2: Input 6/2 = and then press I/Y.
Step 3: Input 40,000 +/- and then press PV.
Step 4: Input 0 and then press PMT.
Step 5: Press CPT FV = 64,188.26.
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© McGraw Hill
19-34
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© McGraw Hill
19-35
Textbook Problem 19-13
Problem Statement:
Melvin Indecision has difficulty deciding whether to put his savings in Mystic Bank
or Four Rivers Bank. Mystic offers 10% interest compounded semiannually. Four
Rivers offers 8% interest compounded quarterly. Melvin has $10,000 to invest. He
expects to withdraw the money at the end of 4 years. Which bank gives Melvin
the better deal? Check your answer. LU 19-1(3)
Solution:
Mystic
Four Rivers
4 years × 2 = 8 periods
4 years × 4 = 16 periods
10%
= 5%
2
8%
= 2%
4
16
$10000 (1 + 0.02 ) = $69152.86
= $13727.86
?10000
= $3727.86
$ 3728.86
$10000 (1 + 0.05 )8 = $14774.55
?10000
$ 4774.55
Access the text alternative for slide images
© McGraw Hill
36
Problem 19-13
Melvin Indecision has difficulty deciding whether to put his savings in Mystic Bank
or Four Rivers Bank. Mystic offers 10% interest compounded semiannually. Four
Rivers offers 8% interest compounded quarterly. Melvin has $10,000
to invest. He expects to withdraw the money at the end of 4 years. Which bank
gives Melvin the better deal? Check your answer. LU 19-1(2)
Solution:
Mystic
Four Rivers
4 years × 2 = 8 periods
4 years × 4 = 16 periods
10% = 5%
2
FV = $10,000(1 + .05)8 = $14,774.55
$14,774.55 ? $10,000 = $4,774.55
8% = 2%
4
FV = $10,000(1 +.02)16 = $13,727.86
$13,727.86 ? $10,000 = $3727.86
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© McGraw Hill
19-37
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© McGraw Hill
19-38
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
© McGraw Hill
19-39
Textbook Problem 19-14
Problem Statement:
Lee Holmes deposited $15,000 in a new savings account at 9% interest
compounded semiannually. At the beginning of year 4, Lee deposits an
additional $40,000 at 9% interest compounded semiannually. At the end
of 6 years, what is the balance in Lees account? LU 19-1(2)
Solution:
Year 1 Beginning of Year 4:
3 years ? 2 = 6 periods
9%
= 4 12 %
2
$15000 (1 + 0.045 ) = $19533.90
6
+40000
$59533.90
Year 4 End of Year 6:
© McGraw Hill
$59533.90 (1 + 0.045 ) = $77528.62
6
Future value
40
Textbook Problem 19-23
Problem Statement:
Paul Havlik promised his grandson Jamie that he would give him $6,000
8 years from today for graduating from high school. Assume money is
worth 6% interest compounded semiannually. What is the present value
of this $6,000? LU 12-2(2).
Solution:
8 years × 2 = 16 periods
6%
= 3%
2
$6,000
(1 + .03)
16
© McGraw Hill
= $3,739
Present Value
41
Paul Havlik promised his grandson Jamie that he would give him $6,000 8 years
from today for graduating from high school. Assume money is worth 6% interest
compounded semiannually. What is the present value of this $6,000?
LU 19-2(2)
Step 1: Input 16 and then press N.
Solution: 8 years × 2 = 16 periods
Step 2: Input 6/2 = and then press I/Y.
6%
Step 3: Input 6000 and then press FV.
2 = 3%
Step 4: Input 0 and then press PMT.
$6,000(1 + .03)16 = $3,739.00
Step 5: Press CPT PV = -3739.00
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© McGraw Hill
19-42
Because learning changes everything.
®
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Because learning changes everything.®
Chapter 10
Instalment Buying and Revolving
Charge Credit Cards
Math for Business and Finance: an Algebraic
Approach, 3rd Edition Jeffrey Slater
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.
Learning Unit Objectives
LU 10-1: Cost of Installment Buying
1. Calculate the amount financed, finance charge, and deferred
payment.
2. Calculate the APR.
3. Calculate the monthly payment.
LU 10-2: Revolving Charge Credit Cards
1. Calculate the finance charges on revolving charge credit card
accounts.
© McGraw Hill
2
Fixing your credit report is important because it can impact the interest
rate you pay and ,may even determine if you get offered a job
car loans are increasing in length. Some are now 8 years
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Education.
© McGraw Hill
10-3
Cost of Installment Buying
Amount financed (AF) the amount actually borrowed.
AF = Cash price ? Down
payment
Deferred payment price (DPP) the total of all monthly payments plus
the down payment.
DPP = Total of all monthly payments + Down payment
Finance charge (FC) the interest charge
FC = Total of all monthly payments ? Amount financed
Installment loan A loan paid off in a series of equal periodic
payments. Payments include interest and principal.
© McGraw Hill
4
Pickup Truck Advertisement
Access the text alternative for slide images.
© McGraw Hill
5
Cost of Installment Buying
Example:
Mary Wilson would like to buy a 4×4 Pickup that cost $9,345. If she puts down
$300 she can finance the balance for 60 months at 10.5% (monthly payment =
$194.38). Calculate the amount financed, finance charge, and deferred payment
price.
Amount financed
=
Cash price
?
Down payment
$9,045
=
$9,345
?
$300
Total finance charge
(interest charge)
$2,617.80
Deferred payment Price
$11,962.80
© McGraw Hill
Total of all monthly
payments
=
$11,662.80
($194.38 × 60)
Amount financed
?
= Total of all monthly +
payments
=
$11,662.80
+
$9,045
Down payments
$300
6
Calculating APR by Formula
APR =
72 ? I
3P(N + 1) + I (N ? 1)
I = Finance charge on the loan
P = Amount financed
N = Number of months of the loan
Example:
The pickup truck advertisement shows APR of 10.5%. We can check this by
formula.
APR =
=
© McGraw Hill
72 ? $2617.80
$188481.60
=
=
3($9045)(60 + 1) + $2617.80(60 1) $1655235 + $154450.20
$188481.60
= .1041516 = 10.4%APR
$1809685.20
7
© McGraw Hill
8
Calculating the Monthly Payment by
Formula
1
Example:
The pickup truck advertisement shows a $194.38 monthly
payment. We can check this by formula and by table lookup.
Monthly Payment Amount =
Finance charge + Amount financed
Number of payments of loan
Monthly Payment Amount =
© McGraw Hill
$2,617.80 + $9,04
= $194.38
60
9
Calculating the Monthly Payment by
Formula
2
3 Steps
1. Calculate the periodic rate in decimal format.
2. Substitute values for N, I, and PV into the formula.
3. Solve the following:
PMT =
PV (I)
1
1?
(1 + I ) N
N = Number of payments
I = Periodic interest rate
PV = Loan amount
PMT = Monthly payment
PMT =
© McGraw Hill
$9,045(.00875)
$79.14375
$79.14375
=
=
= $194.41
1
1 ? .592907762 .407092238
1?
(1 + .00875)60
10
Calculating the Monthly Payment
USING Excel
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Education.
© McGraw Hill
10-11
Sharon got a screaming deal on a 2018 Lexus IS C. She financed
$49,500 at 2% for 5 years. The $49,500 financed included loan charges
of $450
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Education.
© McGraw Hill
10-12
Calculating APR by Table
1
3 Steps
1. Divide the finance charge by amount financed and
multiply by $100 to get the table lookup factor.
2. Go to APR Table 10.1. At the left side of the table are
listed the number of payments that will be made.
3. When you find the number of payments you are looking
for, move to the right and look for the two numbers closest
to the table lookup number. This will indicate the APR.
.
© McGraw Hill
13
Calculating APR by Table
Truth in
Lending Act
APR must be
accurate to
the nearest
1/4 of 1%
2
Calculating APR rate by table:
Finance charge
= $100 = Table 10.1 lookup number
Amount financed
Back to previous example:
Finance charge: $2,617.80
Amount financed: 9,045
$2617.80
? 100 = $28.94( Table)
$9045
APR between 10.25% and
10.50% (refer to next slides)
© McGraw Hill
14
Annual Percentage Rate Table 10.1 per
$100, part 1
Access the text alternative for slide images.
© McGraw Hill
15
Loan Amortization Table (Table 10.2)
(Monthly payment per $1,000 to pay principal and interest on installment
loan)
Terms in months
6
12
18
24
30
36
42
48
54
7.50%
$170.34
$86.76
$58.92
$45.00
$36.66
$31.11
$27.15
$24.18
$21.88
8.00%
170.58
86.99
59.15
45.23
36.89
31.34
27.38
24.42
22.12
8.50%
170.83
87.22
59.37
45.46
37.12
31.57
27.62
24.65
22.36
9.00%
171.20
87.46
59.60
45.69
37.35
31.80
27.85
24.77
22.59
10.00%
171.56
87.92
60.06
46.14
37.81
32.27
28.32
25.36
23.07
10.50%
171.81
88.15
60.29
46.38
38.04
32.50
28.55
25.60
23.32
© McGraw Hill
16
Calculating the Monthly Payment by Table
3 Steps
1. Divide the loan amount by $1,000.
$9, 045
= 9.045
$1, 000
2. Look up the rate (10.5%) and the number of months (60).
At the intersection is the table factor showing the monthly
payment per $1,000 ($21.49).
3. Multiply the quotient in Step 1 by the factor in Step 2.
9.045 × $21.49 = $194.38
© McGraw Hill
17
Revolving Charge Credit Cards
Fair Credit and Charge Card Disclosure Act of 1988.
Interest charges are based on the interest rate times the
previous months balance (outstanding balance).
Payments are first applied towards interest and then the
outstanding balance (US Rule).
Revolving charge account — allows the buyer open-end
credit up to the maximum credit limit.
© McGraw Hill
18
Paying Just the Minimum, and Getting
Nowhere Fast
The cost in years and dollars of paying the minimum 2% of balances on
credit cards charging 17% annual interest:
Balance
Total Cost
Total Time
$1,000
$2,590.35
17 years, 3 months
$2,500
$7,733.49
30 years, 3 months
$5,000
$16,305.34
40 years, 2 months
Source: www.bankrate.com
© McGraw Hill
19
Schedule of Payments (Table 10.1)
Monthly
payment
Number
Outstanding
balance Due
1
$8,000.00
$120.00 (.015 ×
$8,000.00)
2
$7,620.00
3
$7,234.30
© McGraw Hill
1½% interest
Payment
Amount of
monthly
Payment
Reduction in
balance due
Outstanding balance
due
$500.00
$380.00 ($500.00 ?
$120.00)
$7,620.00 ($8,000.00
? $380.00)
$114.30 (.015 ×
$7,620.00)
$500.00
$385.70 ($500.00 ?
$114.30)
$7,234.30 ($7,620.00
? $385.70)
$108.51 (.015 ×
$7,234.30)
$500.00
$391.49 ($500.00 ?
$108.51)
$6,842.81 ($7,234.30
? $391.49)
20
Revolving Charge Credit Cards
Interest charges are based on the interest rate times the previous months
balance (outstanding balance).
Payments are first applied towards interest and then the outstanding balance
(US Rule).
Revolving charge account — allows the buyer open-end credit up to the
maximum credit limit.
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Education.
© McGraw Hill
10-21
To calculate the average daily balance, the credit card company takes the sum of the cardholders
balances at the end of each day in the billing cycle and divides that amount by the total number of days
in the billing cycle.
Then, the company multiplies this figure by the cards annual percentage rate, or APR, to determine
interest charges.
The average daily balance is only used for people who havent paid off their statement balance on time
at the end of the month.
Many people will have a grace period during which they can pay the unpaid balance.
However, on the first day after the end of the grace period, the credit card company will start charging
interest based on the average daily balance.
You won’t be charged interest if a 0% promotional rate applies to your balance. However, once
the promotion is over- You’ll be charged interest whenever you don’t pay the full balance from
the previous billing cycle. For example, if your credit card statement balance is $1,000, you’ll
have to pay the full $1,000 to avoid being charged interest
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Education.
© McGraw Hill
10-22
Calculating Average Daily Balance
1
6 Steps; Steps 1 3
1. Calculate the daily balance or amount owed at the end of each day
during the billing cycle:
Daily balance = Previous balance + Cash advances + Purchases ? Payments ? Credits
2. When the daily balance is the same for more than one day, multiply it
by the number of days the daily balance remained the same or the
number of days of the current balance.
3. Add the cumulative balances.
© McGraw Hill
23
Calculating Average Daily Balance
2
6 Steps; Steps 4 6
4. Divide the sum of the cumulative daily balances by the number of
days in the billing cycle.
5. Calculate the finance charge.
Finance charge = Rate per month × Average daily balance
6. Calculate the new balance.
New Balance = Previous Balance + Cash Advances + Purchases ? Payments ?
Credits + Finance Charge
© McGraw Hill
24
Calculating Outstanding Balance
Example:
Calculate the balance outstanding at the end of month 2 (use U.S. Rule)
given the following: purchased $600 desk; pay back $40 per month; and
charge of 2 ½% interest on unpaid balance.
Month
Balance
due
1
2
© McGraw Hill
Interest
Monthly
payment
Reduction in
balance
Balance
outstanding
$600
$15.00 (.025 × $600)
$40
$25.00 ($40 ?
$15)
$575.00
$575
$14.38 (.025 × $575)
$40
$25.62
$575.00
25
Calculating Average Daily Balance
3
Example:
Calculate the average daily balance and finance charge from the
information that follows.
31-day billing cycle
8/20
Billing date
Previous balance
$210
8/27
Payment Charge:
$50 cr.
8/31
Staples
30
9/5
Payment
10 cr.
9/10
Cash advance
60
Rate = 2% per month on average dally balance.
© McGraw Hill
26
Calculating Average Daily Balance
Step 1 – Calculate the daily
balance at the end of each
day during the billing cycle
Example continued:
31 ? 21 =
Step 2 – When the daily balance is the
same for more than 1 day, multiply it
by the number of days the daily
balance remained the same or the
number of days of the current balance
Days
Current Daily Balance
7
4
5
5
10
31
$210
160 ($210 ? $50)
190 ($160 + $30)
180 ($190 ? $10)
240 ($180 + $60)
Average daily balance =
(7+4+5+5)
© McGraw Hill
4
Extension
$1,470
640
950
900
2,400
$6,360
(210×7)
(160×4)
(190×5)
(180×5)
(240×10)
? Step 3
$6,360
= $205.16 – step 4
31
Finance charge = $205.16 ×.02 = $4.10
– Step 5
27
Textbook Problem 10-16
Problem Statement:
First America Banks monthly payment charge on a 48-month, $20,000 loan is $488.26. The
U.S. Banks monthly payment fee is $497.70 for the same loan amount. What would be the
APR for an auto loan for each of these banks? (Use the Business Math Handbook.) LU
10?1(1, 2)
Solution:
First America Bank
First America Bank
$488.26 × 48 =
U.S. Bank
$23,436.48
$497.70 × 48 =
? 20,000.00
$ 3,436.48
APR =
APR between 8.00% and 8.25%
© McGraw Hill
? 20,000.00
finance charge
72 ? $3436.48
3($20000)( 48 + 1) + $3436.48( 48 ? 1)
= .0798 = 8%
$23,889.60
$ 3,889.60
APR =
finance charge
72 ? $3889.60
3($20000)( 48 + 1) + $3889 + .60( 48 ? 1)
= .0897 = 9%
APR between 8.75% and 9%
28
Textbook Problem 10-17
Problem Statement:
From the following facts, Molly Roe has requested you to calculate the average daily
balance. The customer believes the average daily balance should be $877.67. Respond to
the customers concern. LU 10?2(1)
28-day billing eye
3/18
3/24
3/29
4/5
4/9
Billing date
Payment
Previous balance
Charge: Sears
Payment
Charge: Macy’s
$60 cr.
250
20 cr.
200
$800
Solution:
Number. of Days of Current
Balance
6
5
7
4
6 (28 ? 22)
Current Balance
$ 800
740
990
970
1,170
Extension
$ 4,800
3,700
6,930
3,880
7,020
$26,330 / 28 =
$940.36
Customer divided by 30 days instead of 28 days should be $940.36.
© McGraw Hill
29
Textbook Problem 10-18
Problem Statement:
1
Jill bought a $500 rocking chair. The terms of her revolving charge are 1 2 % on the unpaid
balance from the previous month. If she pays $100 per month, complete a schedule for the
first 3 months like Table 10.3. Be sure to use the U.S. Rule. LU 10-2(1)
Solution:
Jill bought a $500 rocking chair. The terms of her revolving charge are 1 12 % on the unpaid
balance from the previous month. If she pays $100 per month, complete a schedule for
the first 3 months like Table 10.1 (p.264). Be sure to use the U.S. Rule. LU 10-2(1)
Monthly
payment
Number
Outstanding
balance Due
1
$500.00
$7.50 ($500.00 ×
0.15)
2
$470.50
3
$313.61
© McGraw Hill
1½% interest
Payment
Amount of
monthly
Payment
Reduction in balance
due
Outstanding
balance due
$100.00
$92.50 ($100.00 ?
$7.50)
$407.50 ($500.00 ?
$92.50)
$6.11 ($407.50 ×
0.15)
$100.00
$93.89 ($100.00 ?
$6.11)
$3.13.61 ($407.50 ?
$93.89)
$4.70 ($313.61 ×
0.15)
$100.00
$95.30 ($100.00 ?
$4.70)
$218.31 ($313.61 ?
$95.30)
30
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Because learning changes everything.®
Chapter 19
Compound Interest and Present Value
Math for Business and Finance: an Algebraic
Approach, 3rd Edition
Jeffrey Slater
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.
Learning Unit Objectives
LU 19-1: Compound Interest (Future Value) The Big Picture.
1. Compare simple interest with compound interest.
2. Calculate the compound amount and interest manually, by table look
up, using algebraic formulas and with financial calculator.
3. Explain and compute the effective rate (APY).
LU 19-2: Present Value The Big Picture.
1. Compare present value (PV) with compound interest (FV).
2. Compute present value by table look up using algebraic formulas and
with financial calculator.
3. Check the present value answer by compounding.
© McGraw Hill
2
Compounding Interest (Future Value)
Compounding Involves the calculation of interest
periodically over the life of the loan or investment.
Compound Interest The interest on the principal plus the
interest of prior periods.
Future Value (FV) or compound amount The final
amount of the loan or investment at the end of the last
period.
Present Value (PV) The value of a loan or investment
today.
© McGraw Hill
3
Common Compounding Terms
Compounded annually: 1 time a year.
Compounded semiannually: 2 times each year.
Compounded quar
