Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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284 Part 4 Interest Applications
THE BOTTOM LINE
Summary of chapter learning objectives:
Learning Objective
14.1
Convert between annual and monthly interest rates.
Example
1. Convert 0.75% per month to an annual rate.
2. Convert 15% per year to a monthly rate
Answers: 1. 9% per year 2. 1.25% per month 3. $87.50 4. Finance charge, $9.26; new balance, $1,161.40
5. $42 6. 15.75% 7. Payment, $342.14; unpaid balance, $1,672.86 8. $1,289.58
14.2
Compute simple interest on a monthly basis.
3. Compute the simple interest on $2,500 for 7 months at 0.5% per
month (6% per year).
14.3
Compute finance charges for credit account purchases.
4. Charge account terms apply a 1.25% finance charge to the previous
balance, less any payments and credits, but ignoring purchases. Find
the finance charge and new balance when the previous balance is
$1,683.43, payments plus credits total $942.77, and purchases are
$411.48.
14.4
Compute costs of installment purchases.
5. Furniture worth $2,500 is paid for with a $400 down payment and
three payments of $700, plus monthly interest of 1% on the unpaid
balance. Find the total interest paid. The monthly unpaid balances are
$2,100, $1,400, and $700.
14.5
Compute effective rates.
6. A $2,400 purchase is to be repaid in three equal monthly principal
payments of $800 each. There will be one interest payment of $60
(10% of $2,400 for three months) and insurance premiums of $1 each
month. Calculate the effective rate of interest. The monthly unpaid
balances are $2,400, $1,600, and $800.
14.6
Amortize a loan.
7. A $2,000 loan will be amortized over 6 months at an annual rate of
9%. Find the payment, using Table 14-1, and calculate the unpaid bal-
ance after the first month.
14.7
Compute the monthly payment on a home mortgage.
8. A $180,000 home mortgage is for 20 years at 6% annual interest.
Find the monthly payment.
Chapter 14 Installment Purchases 285
1 Change the monthly rates to annual rates.
a. 0.75% 5 b. 0.625% 5 c. 1.2% 5 d. % 5
2 Change the annual rates to monthly rates.
a. 6% 5 b. 15% 5 c. 13.2% 5 d. 9.6% 5
3 A store offers the following credit terms: “There will be no finance charge if the full amount of the new balance is
received on or before the due date. Unpaid balances after the due date will be charged interest based upon the pre-
vious balance, less any payments and credits before the due date. The rates are 1.75% on the first $1,000 of the un-
paid balance and 1.25% on the part of the unpaid balance that exceeds $1,000.”
Calculate (a) the finance charge and (b) the new balance on an account that had a previous balance of
$2,752.88; a payment of $800; credits of $215; and purchases of $622.75.
4 Neta Prefontaine buys $3,000 worth of merchandise. She agrees to pay $1,000 per month on the principal. In addi-
tion, she will pay interest of 1% per month (12% annually) on the unpaid balance. Complete the following table.
Unpaid InterestPrincipal Total New
Month Balance Payment Payment Payment Balance
1 $3,000.00 a. $1,000.00 b. c.
2d. e. $1,000.00 f. g.
3h.i. $1,000.00 j. $0.00
5 Use the results of problem 4 and compute the effective annual interest rate using the formula R 5 , where
P is the average unpaid balance, I is the total interest paid, and T is the period of the loan in years.
6 Use Table 14-1 to find the monthly payment of a $225,000 mortgage that is amortized over 15 years at 4.5%.
7 A $3,000 loan is amortized over 3 months at 12%. The first two monthly payments are $1,020.07; the final pay-
ment may differ. Complete the following table.
Unpaid Interest Total Principal New
Month Balance Payment Payment Payment Balance
1 $3,000.00 a. $1,020.07 b. c.
2d. e. $1,020.07 f. g.
3h.i. j. k. $0.00
I
P 3 T
2
5
SELF-CHECK
Review Problems for Chapter 14
Answers to the Self-Check can be found in Appendix B at the back of the text.
286 Part 4 Interest Applications
Notes
Chapter 14 Installment Purchases 287
Name
Date Score
Learning Objectives
1 2 3
Assignment 14.1 Monthly Finance Charges
A (19 points) Problem 1: Change the rates from annual to monthly. Problem 2: Change the rates from
monthly to annual. (1 point for each correct answer)
1a. 18% 5 b. 15% 5 c. 16.8% 5 d. 7.2% 5
e. 6.6% 5 f. 19.2% 5 g. 14.4% 5 h. 8.4% 5
i. 9% 5 j. 9.6 % 5
2a. 0.5% 5 b. 0.7% 5 c. 1.3% 5 d. 1.25% 5
e. 5 f. 0.75% 5 g. 0.9% 5 h. 1.15% 5
i. 0.4% 5
Score for A (19)
0.4% 3 12
4.8%
1.15% 3 120.9% 3 120.75% 3 12
13.8%10.8%9%9.6%
4
5
%
1.25% 3 121.3% 3 120.7% 3 12
0.5% 3 12
15%15.6%8.4%6%
9.6% 4 129% 4 12
0.8%0.75%
8.4% 4 1214.4% 4 1219.2% 4 126.6% 4 12
0.7%1.2%1.6%0.55%
7.2% 4 1216.8% 4 1215% 4 1218% 4 12
0.6%1.4%1.25%1.5%
5 0.8%
0.8% 3 12
4
5
%
288 Part 4 Interest Applications
Assignment 14.1 Continued
B (33 points) Lakeside Furniture Store offers the credit terms shown below to its retail customers. In
problems 3–5 compute the finance charge, if any, and the new balance. Assume that all payments are
made within the current billing cycle. (3 points for each correct answer)
TERMS: There will be no finance charge if the full amount of the new balance is received within 25 days after the
cycle-closing date. The finance charge, if any, is based upon the entire previous balance before any payments or credits
are deducted. The rates are 1.5% per month on amounts up to $1,000 and 1.25% on amounts in excess of $1,000. These
are annual percentage rates of 18% and 15%, respectively.
Cycle Previous Payment Finance New
Closing Balance Amount Credits Charge Purchases Balance
3. 3/20/2022 $2,147.12 $900.00 $175.50 $647.72
4. 6/20/2022 $943.72 $250.00 $35.00 $412.99
5. 9/20/2022 $3,412.27 $3,000.00 $212.98 $907.51
$3,412.27 2 $3,000.00 2 $212.98 1 $45.15 1 $907.51 5 $1,151.95
$15.00 1 $30.15 5 $45.150.0125 3 $2,412.27 5 $30.150.015 3 $1,000 5 $15.00
$1,151.95$45.15
$943.72 2 $250.00 2 $35.00 1 $14.16 1 $412.99 5 $1,085.87
0.015 3 $943.72 5 $14.16
$1,085.87$14.16
$2,147.12 2 $900.00 2 $175.50 1 $29.34 1 $647.72 5 $1748.68
$15.00 1 $14.34 5 $29.340.0125 3 $1,147.12 5 $14.340.015 3 $1,000 5 $15.00
$1,748.68$29.34
Chapter 14 Installment Purchases 289
Assignment 14.1 Continued
In problems 6 and 7, Lelia McDaniel has an account at Lakeside Furniture Store. Compute the missing values in Lelia’s
account summary for the months of August and September. The previous balance in September is the same as the new
balance in August.
Cycle Previous Payment Finance New
Closing Balance Amount Credits Charge Purchases Balance
6. 8/20/2022 $1,636.55 $900.00 $ 36.00 $966.75
7. 9/20/2022 $1,200.00 $109.75 $589.41
Score for B (33)
C (48 points) Devlin’s Feed & Fuel offers the credit terms shown below to its retail customers. In problems
8-12 compute the missing values in the charge accounts shown. Assume that all payments are made
within 30 days of the billing date. (3 points for each correct answer)
TERMS: Finance Charge is based on the Net Balance, if any payment is received within 30 days of the billing date. If
payment is made after 30 days, then the Finance Charge is based on the Previous Balance. Net Balance equals Previous
Balance less Payments and Credits. In either case, the monthly rate is 1.25% on the first $500 and 1% on any amount
over $500. These are annual percentage rates of 15% and 12%, respectively.
Billing Previous Payment Net Finance New New
Date Balance Amount Credit Balance Charge Purchases Balance
8. 4/25/2022 $2,621.05 $1,700.00 $0.00 $751.16
$921.05 1 10.46 1 $751.16 5 $1,682.67$6.25 1 $4.21 5 $10.46
0.01 3 $421.05 5 $4.210.0125 3 $500 5 $6.25$2,621.05 2 $1,700.00 5 $921.05
$1,682.67$10.46$921.05
$1,690.26 2 $1,200.00 2 $109.75 1 $23.63 1 $589.41 5 $993.55
$15.00 1 $8.63 5 $23.630.0125 3 $690.26 5 $8.630.015 3 $1,000 5 $15
$993.55$23.63$1,690.26
$1,636.55 2 $900.00 2 $36.00 1 $22.96 1 $966.75 5 $1,690.26
$15.00 1 $7.96 5 $22.960.0125 3 $636.55 5 $7.960.015 3 $1,000 5 $15.00
$1,690.26$22.96
290 Part 4 Interest Applications
Assignment 14.1 Continued
Billing Previous Payment Net Finance New New
Date Balance Amount Credit Balance Charge Purchases Balance
9. 3/25/2022 $1,827.15 $700.00 $28.75 $672.39
10. 11/25/2022 $1,019.63 $325.00 $26.50 $218.75
In problems 11 and 12 compute the missing values in Jimmy Petrasek’s charge account summary at Devlin’s for the
months of June and July. The previous balance in July is the same as the new balance in June.
11. 6/25/2022 $1,352.12 $500.00 $62.00 $772.35
12. 7/25/2022 $600.00 $67.77 $743.95
Score for C (48)
$903.85 1 $10.29 1 $743.95 5 $1,658.09$6.25 1 $4.04 5 $10.29
0.01 3 $403.85 5 $4.040.0125 3 $500 5 $6.25$1,571.62 2 $600.00 2 $67.77 5 $903.85
$1,658.09$10.29$903.85$1,571.62
$790.12 1 9.15 1 $772.35 5 $1,571.62$6.25 1 $2.90 5 $9.15
0.01 3 $290.12 5 $2.900.0125 3 $500 5 $6.25$1,352.12 2 $500.00 2 $62 5 $790.12
$1,571.62$9.15$790.12
$668.13 1 $7.93 1 $218.75 5 $894.81$6.25 1 $1.68 5 $7.93
0.01 3 $168.13 5 $1.680.0125 3 $500 5 $6.25$1,019.63 2 $325.00 2 $26.50 5 $668.13
$894.81$7.93$668.13
$1,098.40 1 $12.23 1 $672.39 5 $1,783.02$6.25 1 $5.98 5 $12.23
$0.01 3 $598.40 5 $5.980.0125 3 $500 5 $6.25$1,827.15 2 $700.00 2 $28.75 5 $1,098.40
$1,783.02$12.23$1,098.40
Chapter 14 Installment Purchases 291
Assignment 14.2 Installment Sales and Effective Rates
Name
Date Score
A (60 points) Hal Layer needed to purchase office equipment costing $4,800. He was able to finance his
purchase over 3 months at a 9% annual interest rate. Following are three different payment options
under these conditions. Complete the installment purchase table for each payment option. (2 points for
each correct answer)
1. Hal pays $1,600 per month on the principal and pays interest of 0.75% on the unpaid balance each month
(9% annual rate).
Unpaid InterestPrincipal Total New
Month Balance Payment Payment Payment Balance
1 $4,800.00 $1,600.00
2 1,600.00
3 1,600.00 0.00
$4,800.00
2. Hal makes monthly payments of $1,400, $1,400, and $2,000 on the principal and pays interest of 0.75%
on the unpaid balance each month (9% annual rate).
Unpaid InterestPrincipal Total New
Month Balance Payment Payment Payment Balance
1 $4,800.00 $1,400.00
2 1,400.00
3 2,000.00 0.00
$4,800.00
3. Hal pays $1,600 per month on the principal. The total interest charge is 9% of the original principal for
3 months. Bob pays of the total interest each month.
Unpaid InterestPrincipal Total New
Month Balance Payment Payment Payment Balance
1 $4,800.00 $1,600.00
2 1,600.00
3 1,600.00 0.00
$4,800.00
Score for A (60)
1,636.0036.001,600.00
1,600.001,636.0036.003,200.00
$3,200.00$1,636.00$36.00
1
3
2,015.0015.002,000.00
2,000.001,425.5025.503,400.00
$3,400.00$1,436.00$36.00
1,612.0012.001,600.00
1,600.001,624.0024.003,200.00
$3,200.00$1,636.00$36.00
Learning Objectives
4 5
$4,800 3 0.0075 5 $36 $1,600 1 $36 5 $1,636 $4,800 2 $1,600 5 $3,200
$3,200 3 0.0075 5 $24 $1,600 1 $24 5 $1,624 $3,200 2 $1,600 5 $1,600
$1,600 3 0.0075 5 $12 $1,600 1 $12 5 $1,612 $1,600 2 $1,600 5 $0
$4,800 3 0.0075 5 $36.00 $1,400 1 $36 5 $1,436 $4,800 2 $1,400 5 $3,400
$3,400 3 0.0075 5 $25.50 $1,400 1 $25.50 5 $1,425.50 $3,400 2 $1,400 5 $2,000
$2,000 3 0.0075 5 $15 $2,000 1 $15 5 $2,015 $2,000 2 $2,000 5 $0
I 5 P 3 R 3 T 5 $4,800 3 0.09 35$108 total interest $4,800 2 $1,600 5 $3,200
$108 4 3 5 $36 per month $3,200 2 $1,600 5 $1,600
$1,600 1 $36 5 $1,636 per month $1,600 2 $1,600 5 $0
3
12
292 Part 4 Interest Applications
Assignment 14.2 Continued
B (40 points) For each of the following problems calculate the effective rate using the formula .
(Points for each correct answer as shown)
4. Compute R 5 effective rate for the table in problem 1 in part A, with P 5 average unpaid balance,
I 5 total interest charge and year.
a. P 5 Average unpaid balance (3 pts)
b. I 5 Total interest charge (3 pts)
c. R 5 Effective interest rate (4 pts)
5. Compute R 5 effective rate for the table in problem 1 in part A, with P 5 average unpaid balance,
I 5 total finance charge, and year. The finance charge is the total interest, plus a loan origination fee
of of the original principal, plus $7.50 of insurance premiums ($2.50 per month).
a. P 5 Average unpaid balance (3 pts)
b. I 5 Total finance charge (3 pts)
c. R 5 Effective interest rate (4 pts)
6. Compute R 5 effective rate for the table in problem 2 in part A, with P 5 average unpaid balance,
I 5 total interest charge, and year.
a. P 5 Average unpaid balance (3 pts)
b. I 5 Total interest charge (3 pts)
c. R 5 Effective interest rate (4 pts)
7. Compute R 5 effective rate for the table in problem 3 in part A, with P 5 average unpaid balance,
I 5 total interest charge, and year.
a. P 5 Average unpaid balance (3 pts)
b. I 5 Total interest charge (3 pts)
c. R 5 Effective interest rate (4 pts)
Score for B (40)
13.5%
$108
$3,200
T 5
3
12
9%
$76.50
$3,400
T 5
3
12
14.4%
$115.50
$3,200
3
4
%
T
5
3
12
9%
$72
$3,200
T 5
3
12
R 5
I
P 3 T
P 5
I 5 $36 1 $24 1 $12 5 $72
R 5 0.09, or 9%
I
P 3 T
5
$72
$3,200 3
3
12
5
$72
$800
5
$4,800 1 $3,200 1 $1,600
3
5
$9,600
3
5 $3,200
P 5 $3,200 Loan fee 5 0.0075 3 $4,800 5 $36
I 5 Interest 1 Loan fee 1 Insurance 5 $72 1 $36 1 $7.50 5 $115.50
R 5 0.1444, or 14.4%
I
P 3 T
5
$115.50
$3,200 3
3
12
5
$115.50
$800
5
P 5
I 5 $36 1 $25.50 1 $15 5 $76.50
R 5 0.09, or 9%
I
P 3 T
5
$76.50
$3,400 3
3
12
5
$76.50
$850
5
$4,800 1 $3,400 1 $2,000
3
5
$10,200
3
5 $3,400
P 5
I 5 $36 1 $36 1 $36 5 $108, or I 5 $4,800 3 0.09 35$108
R 5 0.135, or 13.5%
I
P 3 T
5
$108
$3,200 3
3
12
5
$108
$800
5
3
12
$4,800 1 $3,200 1 $1,600
3
5
$9,600
3
5 $3,200
Chapter 14 Installment Purchases 293
Assignment 14.3 Amortization and Mortgages
Name
Date Score
6
Learning Objectives
7
A (16 points) Lincoln Lending Corp. amortizes all of its mortgage loans and many of its personal loans on
a monthly basis.The total monthly payments are equal each month and include both interest and prin-
cipal. Use Table 14-1 to find the amortization payment factor for each loan.Then compute the monthly
payment. (2 points for each correct answer)
Amortization
Loan and Terms of Amortization Payment Factor Monthly Payment
1. $18,000 over 5 months at 9%
2. $27,000 over 3 years at 7.5%
3. $275,000 over 20 years at 4.5%
4. $150,000 over 15 years at 6%
B (32 points) On April 13, Braunda Johannesen borrowed $6,000 from her bank to help pay her federal
income taxes for the previous year. The bank amortized her loan over 4 months at an annual rate of 9%.
Braunda paid interest of 0.75% of the unpaid balance each month. Find the amortization payment fac-
tor in Table 14-1.This factor makes a total payment of $1,528.23 each month except the last. For the last
month, the total payment is the interest payment plus the unpaid balance. Complete the following
amortization schedule. (2 points for each correct answer)
5.
Amortization factor from Table 14-1:
Multiply the amortization factor by 6 to get the total payment shown for months 1, 2, and 3.
Unpaid Interest Total Principal New
Month Balance Payment Payment Payment Balance
6. 1 $6,000.00 $1,528.23
7. 2 1,528.23
8. 3 1,528.23
9. 4 0.00
Score for B (32)
1,516.861,528.2411.381,516.86
1,516.861,505.5622.673,022.42
3,022.421,494.3533.884,516.77
$4,516.77$1,483.23$45.00
$254.70501
$1,265.79$ 8.43857
$1,739.78$ 6.32649
$ 839.87$ 31.10622
$3,681.40$204.52242
$18,000 4 $1,000 5 18
18 3 $204.52242 5 $3,681.40356, or $3,681.40
$27,000 4 $1,000 5 27
27 3 $31.10622 5 $839.86794, or $839.87
$275,000 4 $1,000 5 275
275 3 $6.32649 5 $1,739.78475, or $1,739.78
$150,000 4 $1,000 5 150
150 3 $8.43857 5 $1,265.7855, or $1,265.79
$6,000.00 3 0.0075 5 $45.00; $1,528.23 2 $45.00 5 $1,483.23; $6,000.00 2 $1,483.23 5 $4,516.77
$4,516.77 3 0.0075 5 $33.88; $1,528.23 2 $33.88 5 $1,494.35; $4,516.77 2 $1,494.35 5 $3,022.42
$3,022.42 3 0.0075 5 $22.67; $1,528.23 2 $22.67 5 $1,505.56; $3,022.42 2 $1,505.56 5 $1,516.86
$1,516.86 3 0.0075 5 $11.38; $1,516.86 1 $11.38 5 $1,528.24; $1,516.86 2 $1,516.86 5 0.00
Score for A (16)