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8-12. Solution:
Maxim Air Filters Inc.
Effective rate of interest with 20% compensating balance =
Interest rate 10% 10% 12.5%
1 C 1 .2 .8
or
Interest Days of the year (360)
Principal Compensating balance Days loan is outstanding
$30, 000 $30,000
1 1 12.5%
$300,000 $60,000 $240,000
13. Compensating balances (LO2) Digital Access Inc. needs $400,000 in funds for a project.
a. With a compensating balance requirement of 20 percent, how much will the firm need
to borrow?
b. Given your answer to part a and a stated interest rate of 9 percent on the total amount
borrowed, what is the effective rate on the $400,000 actually being used?
8-13. Solution:
Digital Access Inc.
a.
Amount needed
Amount to be borrowed = 1 C
$400,000 $400, 000
1 .20 .80
$500, 000
b.
$500,000 Total amount borrowed
9% Interest rate
$ 45,000 Interest
$45,000 11.5%
$400,000
14. Compensating balances and installment loans (LO2) Carey Company is borrowing
$200,000 for one year at 12 percent from Second Intrastate Bank. The bank requires a 20
percent compensating balance. What is the effective rate of interest? What would the
effective rate be if Carey were required to make 12 equal monthly payments to retire the
loan? The principal, as used in Formula 8–6, refers to funds the firm can effectively utilize
(Amount borrowed – Compensating balance).
8-14. Solution:
Carey Company
Effective rate of interest with 20% compensating balance =
Interest Days in the year (360)
Principal Compensating balance Days loan is outstanding
$24,000 360 $24,000 360 15%
$200,000 $40,000 360 $160,000 360
Installment loan with compensating balance
( )
( ) ( )
2 Annual no. payments Interest
Total no. of payments + 1 Principal
2 12 $24,000
12 1 $200,000 $40,000
$576,000 $576,000 27.69%
13 $160,000 $2,080,000
´ ´
´
´ ´
=+ ´ -
= = =
´
15. Compensating balances with idle cash balances (LO2) Randall Corporation plans to
borrow $233,000 for one year at 20 percent from the Waco State Bank. There is a 21
percent compensating balance requirement. Randall Corporation keeps minimum
transaction balances of $17,500 in the normal course of business. This idle cash counts
toward meeting the compensating balance requirement. What is the effective rate of
interest?
8-15. Solution:
Randall Corporation
Effective rate of interest =
Interest Days in the year (360)
Principal Compensating balance Days loan is outstanding
$46,600 360 $46,600 23.12%
$233, 000 $31, 430 * 360 $201,570
* $48, 930 $17,500 $31, 430- =
Required compensating balance Minimum balance on
deposit Additional funds needed at bank
16. Compensating balances with idle cash balances (LO2) The treasurer for the Macon Blue
Sox baseball team is seeking a $23,600 loan for one year from the 4th National Bank of
Macon. The stated interest rate is 10 percent, and there is a 15 percent compensating
balance requirement. The treasurer always keeps a minimum of $2,280 in the baseball
team’s checking accounts. These funds count toward meeting any compensating balance
requirements. What will be the effective rate of interest on this loan?
8-16. Solution:
Macon Blue Sox Baseball Team
Effective rate of interest =
Interest Days in the year (360)
Principal Compensating balance Days loan is outstanding
$2,360 360 $2,360 10.56%
$23, 600 $1, 260 * 360 $22,340
* $3,540 $2, 280 $1, 260- =
Required compensating balance Minimum balance on
17. Effective rate under different terms (LO2) Your company plans to borrow $13 million
for 12 months, and your banker gives you a stated rate of 24 percent interest. You would
like to know the effective rate of interest for the following types of loans. (Each of the
following parts stands alone.)
a. Simple 24 percent interest with a 10 percent compensating balance.
b. Discounted interest.
c. An installment loan (12 payments).
d. Discounted interest with a 5 percent compensating balance.
8-17. Solution:
a. Simple interest with a 10% compensating balance
$3,120,000 $3,120,000
1 26.67%
$13,000,000 $1,300,000 $11,700,000
b. Discounted interest
$3,120,000 $3,120,000
1 31.58%
$13,000,000 $3,120,000 $9,880,000
c. An installment loan with 12 payments
2 12 $3,120,000 $74,880,000 44.31%
13 $13, 000,000 $169,000,000
´ ´ = =
´
d. Discounted interest with a 5% compensating balance
( )
$3,120,000 / $13,000,000 – $3,120,000 – $650,000
$3,120,000/$9,230,000 = 33.80%
18. Effective rate under different terms (LO2) If you borrow $5,300 at $400 interest for one
year, what is your effective interest rate for the following payment plans?
a. Annual payment.
b. Semiannual payments.
c. Quarterly payments.
d. Monthly payments.
8-18. Solution:
a. $400/$5,300 = 7.55%
19. Effective rate under different terms (LO2) Zerox Copying Company plans to borrow
$172,000. New Jersey National Bank will lend the money at one-half percentage point over
the prime rate at the time of 17½ percent (18 percent total) and requires a compensating
balance of 21 percent. The principal in this case will be funds that the firm can effectively
use in the business. This loan is for one year. What is the effective rate of interest? What
would the effective rate be if Zerox were required to make four quarterly payments to retire
the loan?
8.19. Solution:
Zerox Copying Company
Effective rates of interest with compensating balance
First determine interest
Then determine the rate
$30,960 $30,960
1 22.78%
$172, 000 36,120 $135,880
´ = =
-
Effective rate of interest with compensating balance and four
quarterly payments.
2 4 $30,960 $247,680 36.46%
(4 1) $135,880 $679, 400
´ ´ = =
+ ´
20. Installment loan for multiyears (LO2) Lewis and Clark Camping Supplies Inc. is
borrowing $51,000 from Western State Bank. The total interest is $15,700. The loan will be
paid by making equal monthly payments for the next three years. What is the effective rate
of interest on this installment loan?
8-20. Solution:
Lewis and Clark Camping Supplies
Rate on installment loan =
( )
( )
2 Annual no. of payments Interest
Total no. of payments + 1 Principal
2 12 $15, 700 $376,800 19.97%
36 1 $51,000 $1,887,000
+
21. Cash discount under special circumstance (LO2) Mr. Hugh Warner is a very cautious
businessman. His supplier offers trade credit terms of 3/15, net 85. Mr. Warner never takes the
discount offered, but he pays his suppliers in 75 days rather than the 85 days allowed so he is
sure the payments are never late. What is Mr. Warner’s cost of not taking the cash discount?
8-21. Solution:
Hugh Warner
Discount % 360
Cost of not taking =
a cash discount 100% Disc.% Final duedate
Discount period
3% 360
100% 3% (75 15)
3.09% 6 18.54%
In this problem, Mr. Warner has the use of funds for 60 extra days
(75 – 15), instead of 70 extra days allowed by the credit terms (85
22. Bank loan to take cash discount (LO1 and 2) The Reynolds Corporation buys from its
suppliers on terms of 3/17, net 45. Reynolds has not been utilizing the discounts offered
and has been taking 45 days to pay its bills.
Mr. Duke, Reynolds Corporation vice president, has suggested that the company begin to
take the discounts offered. Duke proposes that the company borrow from its bank at a
stated rate of 16 percent. The bank requires a 27 percent compensating balance on these
loans. Current account balances would not be available to meet any of this compensating
balance requirement.
Do you agree with Duke’s proposal?
8-22. Solution:
Reynolds Corporation
Discount % 360
Cost of not taking a cash =
discount 100% Disc.% Final due date
Discount period
3% 360 3.09% 12.86 39.74%
97% (45 17)
´
- -
= ´ = ´ =
-
Effective rate of interest with a 27 percent compensating balance
requirement:
The effective cost of the loan, 21.92 percent, is less than the cost
23. Bank loan to take cash discount (LO1 and 2) The Reynolds Corporation buys from its
suppliers on terms of 3/17, net 45. Reynolds has not been utilizing the discounts offered
and has been taking 45 days to pay its bills.
Mr. Duke, Vice President of Reynolds Corporation, has suggested that the company begin
to take the discounts offered. Duke proposes that the company borrow from its bank at a
stated rate of 16 percent. The bank requires a 20 percent compensating balance on these
loans. Current account balances would not be available to meet any of this compensating
balance requirement.
Do you agree with Duke’s proposal?
8.23. Solution:
Reynolds Corporation
Discount % 360
Cost of not taking a cash =
discount 100% Disc.% Final due date
Discount period
3% 360 3.09% 12.86 39.74%
97% (45 17)
´
- -
= ´ = ´ =
-
Effective rate of interest with a 20 percent compensating balance
requirement:
Interest rate 16% 16% 20.00%
1 C 1 .20 .8
The answer now changes. The effective cost of the loan, 20.00 percent, is less than the cost of
passing up the discount, 39.74 percent. Reynolds Corporation should borrow the funds and
pay early to take the discount.
24. Bank loan to take cash discount (LO1 and 2) Neveready Flashlights Inc. needs $340,000
to take a cash discount of 3/17, net 72. A banker will lend the money for 55 days at an
interest cost of $10,400.
a. What is the effective rate on the bank loan?
b. How much would it cost (in percentage terms) if the firm did not take the cash
discount, but paid the bill in 72 days instead of 17 days?
c. Should the firm borrow the money to take the discount?
d. If the banker requires a 20 percent compensating balance, how much must the firm
borrow to end up with the $340,000?
e. What would be the effective interest rate in part d if the interest charge for 55 days
were $13,000? Should the firm borrow with the 20 percent compensating balance?
(The firm has no funds to count against the compensating balance requirement.)
