Business Mathematics: Interest and Discount - Promissory Notes And Bank Discount

A promissory note is a written promise by a debtor, called the maker of the note, to pay the creditor, called the payee of the note, a sum of money on a specified date. Promissory notes are used when money is borrowed or goods or services are sold on credit.

There are two types of promissory notes, interest-bearing notes and non-interest-bearing notes.

The figure below is an example of an interest-bearing note.


Looking at the promissory note in the figure above we learn the following terms:

1. The face value of the note, which is the amount of money stated in the note ($2,000)

2. The date of the note (June 14, 2001), which is the date on which the note was made and from which the interest is computed

3. The term of the note (2 months)

4. The payee of the note (Sunshine Supply Company)

5. The maker of the note (I. J. Franks)

6. The interest rate on the note (14% ordinary simple interest)

7. The maturity date of the note (August 14, 2001, 2 months after June 14, 2001)
On the maturity date, August 14, 2001, the principal of $2,000 and the simple interest at 14% for 2 months must be paid. The total of principal and interest is called the maturity value of the note. (If the term of the note is in days, ordinary simple interest is used to calculate the maturity value.)

The figure below is an example of a non-interest-bearing note.
The interest rate is not stated on the note below. The maturity value of the note is equal to its face value and $500 must be paid on May 9, 2001 (assuming a nonleap year).

Note that interest is paid on a non-interest-bearing loan. The interest is deducted in advance, at the time the money is borrowed.

An important feature of a promissory note is that it is negotiable. That is, it can be transferred to another payee (a person, company, bank) by the endorsement of the present payee. Cashing a note at a bank is called discounting a note. The bank collects interest in advance, called bank discount (D), which is computed on the maturity value (S) of the note at a specified annual discount rate (d) for the term (t) of the discount in years. The term of the discount is the time (in years) from the date of discount until the maturity date of the note. If the time is given in days, the banker’s year of 360 days is used.

Thus the bank discount (D) is computed by
Discount = maturity value × discount rate × term of discount
D = Sdt

The money received for the discounted note is called the proceeds. The proceeds (P) are obtained by deducting the bank discount (D) from the maturity value (S) of the note:

Proceeds = maturity value - bank discount
P = S — D

By combining the preceding two formulas, we can calculate proceeds directly from the discount rate and the term:
P = S – D = S – Sdt = S(1 - dt)

Example
Refer to the above figure: If the First National Bank of Seattle charged 18.5% interest in advance on the 90-day, $500 loan, how much did John Kemp actually receive?

The interest collected in advance is called the bank discount (D):

The money received for the discounted note is called the proceeds (P):

John Kemp received $476.87.
We can rewrite the preceding formula to solve for S:

This formula is used to calculate the maturity value of a loan for specified proceeds.

Example
Celeste Curtis wants to get a 180-day, non-interest-bearing note from a bank that charges 14|% interest. What should be the face value of the note if Celeste needs $1,000 in cash?
We want to find the maturity value (S) of the 180-day note for specified proceeds (P) of $1,000.

The face value of the note should be $1,076.72.

Solved Problems:

5.1Find the maturity value of the note in Fig. 5.1.
Solution

From Sec. 5.4:


5.22 Sunshine Supply Company cashed the note in Fig. 5.1 on July 17 at their bank at a 12% bank discount rate. Find the bank discount and the proceeds.
 

Solution
The term of discount is the time from July 17 to August 14, that is, 28 days.

The bank discount charged by the bank is $19.10 and Sunshine Supply Company receives proceeds of $2,027.57.

5.23   What rate of interest did the bank in Prob. 5.22 realize on its investment if it held the note until the maturity date?
 

Solution
The bank paid $2,027.57 for the note on July 17 and received $2,046.67 from I. J. Franks on August 14. The bank realized a profit of $2,046.67 — $2,027.57 = $19.10 on their investment of $2,027.57 over a period of 28 days. The rate of interest realized by the bank is

Note that the interest rate is 0.11% higher than the corresponding discount rate (d). This is because the discount rate (d) is applied to the maturity value (5), whereas the interest rate (r) is applied to the principal (proceeds) (P). Both rates result in the same amount of interest $19.10 and are said to be equivalent rates.

5.24   Referring to the note in Fig. 5.2, find the proceeds to John Kemp if the First National Bank of Seattle charged 15% interest in advance on the loan.
 

Solution


5.25   What is the true interest rate (at ordinary simple interest) that John Kemp paid on his loan in Prob. 5.24?
 

Solution


5.26   Find the maturity date and the term of discount for each of the following:

Solution

More Problems:

5.27 Find the simple interest on a loan of (a) $500 at 83% for 1 year, (b) $2,000 at 16\% for 30 months, and (c) $1,200 at 10.82% for 6 months.

5.28 Find the ordinary simple interest on a loan of (a) $900 at 14^% for 120 days, (b) $1,400 at 13% for 90 days, and (c) $750 at 9.21% for 60 days.

5.29 Find the exact simple interest on each loan in Prob. 5.28.

5.30 Find the exact time from (a) April 21 to June 29 of the same year, (b) November 7 to February 28 of the following year, (c) March 17, 2000 to November 8, 2000, and (d) July 8, 2000, to January 18, 2001.

5.31 Find the approximate time for each term in Prob. 5.30.

5.32 Find the maturity date of (a) a 90-day loan dated August 17, (b) a 60-day loan dated December 8, (c) a 6-month loan dated May 3, and (d) a 182-day loan dated March 7.

5.33 5.33 Using the four methods (exact time and ordinary interest, exact time and exact interest, approximate time and ordinary interest, and approximate time and exact interest), find the simple interest on (a) an $800 loan at 17% from April 21 to June 29 and (b) a $5,000 loan at 12|% from July 8, 2000, to January 18, 2001.

5.34 5.34 Using the banker’s rule, find the simple interest on investments of (a) $1,500 at 9% from March 17, 2000 to November 8, 2000, (b) $650 at I5j% from October 1,2000, to January 29,2001, (c) $2,000 at lOf % from March 15, 2001, to September 3, 2001.

5.35 Using exact time and exact interest, find the simple interest on the investments in Prob. 5.34.

5.36 Find the maturity value of (a) a $2,500 loan for 85 days, (b) a $1,200 loan for 120 days, and (c) a $10,000 loan for 60 days, all at 14% ordinary simple interest.

5.37 Find the maturity value of the loans in Prob. 5.36 at 12% exact simple interest.

5.38 At what rate of simple interest will (a) $500 accumulate $10 interest in 2 months, (b) money double itself in 7 years, and (c) $2,000 grow to $2,100 in 1 year.

5.39 Find the rate of ordinary simple interest charged on the following loans:


5.40 Freda invested $1,200 for 180 days and earned $65.10 interest. What rate of exact simple interest did she earn?

5.41 5.41 How many days will it take $1,000 (a) to earn $50 at 12% ordinary simple interest and (b) to accumulate to at least $1,500 at 18|% exact simple interest?

5.42 What principal will earn (a) ordinary simple interest of $25 at 12.5% in 120 days, (b) exact simple interest of $19.50 at 9.75% in 73 days, and (c) simple interest of $21.25 at 10% in 3 months?

5.43 Find the principal and the interest on the following loans at ordinary simple interest:


5.44 A couple borrows $20,000. The annual interest rate is 12|%, payable monthly, and the monthly payment is $300. How much of the first payment goes to interest and how much to principal?

5.45 Questions (a) through (e) refer to Fig. 5.3.
   (a)  Who is the maker of the note?
   (b)  What is the face value?
   (c)  What is the maturity date of the note?
   (d)  Who is the payee?
   (e)  What is the maturity value of the note?


5.46 Find the maturity date and the maturity value of each of the following promissory notes:


5.47 Referring to Fig. 5.3, in Prob. 5.45, find the proceeds to Robert Gilbert if Jennifer Brown charged him 18% interest in advance.

5.48 Jennifer Brown cashed the note in Prob. 5.45 on December 20, at a 14% bank discount rate. Find the bank discount and the proceeds.

5.49 Find the maturity date and the term of discount for each of the following notes:


5.50 Find the proceeds when each of the following notes is discounted:


5.51 A bank charges 11% interest in advance on short-term loans. Find the proceeds of the loan if the borrower signs a non-interest-bearing note for (a) $1,800 due in 6 months and (b) $600 due in 90 days.

5.52 A bank charges 15|% interest in advance on short-term loans. Find the face value of the non-interest- bearing note given the bank if the borrower receives (a) $800 for 4 months, (b) $1,200 for 90 days, and (c) $2,000 from June 12 to December 12.

5.53 The Travelers Trust discounted at 15% bank discount a non-interest-bearing note for $20,000 due in 180 days. On the same day the note was discounted again at 14% bank discount at a Federal Reserve bank. Find the profit made by the Travelers Trust.

5.54 On June 29, a retailer buys goods worth $3,000. To take advantage of a 5% cash discount, the retailer signs a 60-day non-interest-bearing note at his bank. The bank charges 11% interest in advance on short-term loans. What should be the face value of this note to give the retailer the exact amount needed to pay cash for the goods?

Answers to Problems:

5.27 (a) $41.25, (b) $825, (c) $64.92
5.28 (a) $43.50, (b) $45.50, (c) $11.51
5.29 (a) $42.90, (b) $44.88, (c) $11.35
5.30 (a) 69 days, (b) 113 days, (c) 236 days, (d) 194 days
5.31 (a) 68 days, (b) 111 days, (c) 231 days, (d) 190 days
5.32 (a) November 15, (b) February 6, (c) November 3, (d) September 5
5.33 (a) $26.07, $25.71, $25.69, $25.34; (b) $343.54, $338.84, $336.46, $331.85
5.34 (a) $88.50, (b) $33.58, (c) $101.53
5.35 (a) $87.29, (b) $33.12, (c) $100.14
5.36 (a) $2,582.64, (b) $1,256, (c) $10,233.33
5.37 (a) $2,569.86, (b) $1,247.34, (c) $10,197.26
5.38 (a) 12%, (b) 14.29%, (c) 5%
5.39 (a) 15$%, (b) 12\%
5.40 11%
5.41 (a) 150 days, (b) 974 days
5.42 (a) $600, (b) $1,000, (c) $850
5.43 (a) P = $780,1 = $76.40; (b) P = $10,000, / = $1,748.96; (c) P = $1,800,1 = $31.25
5.44 I = $208.33, P = $91.67
5.45 (a) Robert Gilbert, (b) $1,500, (c) February 3, 2001, (d) Jennifer Brown, (e) $1,500
5.46 (a) Feb. 3, $765.47; (b) Oct. 16, $2,116.67; (c) Aug. 12, $5,524.43
5.47 $1,455
5.48 D = $26.25, P = $1,473.75
5.49 (a) Oct. 31, t = 24 days; (b) Apr. 4, t = 34 days; (c) June 24, t = 115 days
5.50 (a) $2,945.33, (b) $1,218.90, (c) $498.46, (d) $3,967.89
5.51 (a) $1,701, (b) $583.50
5.52 (a) $842.84, (b) $1,247.56, (c) $2,168.07
5.53 $100
5.54 $2,903.23