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WealthWiseGuys Practical Mathematics

Chapter 11

Promissory Notes and Financial Obligations

Read a written promise, count the term, and calculate what is owed.

A promissory note turns a borrowing arrangement into a written schedule of obligations. This chapter connects the words on a note to dates, interest, discount proceeds, and payment records. All notes, people, rates, fees, and legal arrangements are hypothetical teaching examples, not legal advice or current law; round money to cents unless stated otherwise.

11.1

Reading Notes and Finding Maturity Dates

Learning objectives

After this section you will be able to:

  1. Identify the parties and key terms on a note.
  2. Find a due date for a day-based note.
  3. Calculate maturity value under a specified convention.

Real-life situation

A food-cart equipment note

A Philadelphia food-cart operator signs a 60-day note for equipment. The document states the annual rate, day-count basis, and single maturity payment.

A food-cart equipment note

  • Maker: neighborhood food-cart operator; payee: equipment seller
  • Dated April 10; term: 60 days
  • Principal $2,000.00; simple annual rate 9%; actual/360
  • Due June 9; interest $30.00; maturity value $2,030.00
Figure 11.1 A food-cart equipment note (hypothetical)

The concept

A promissory note is a written promise to pay a specified amount under specified terms. The maker promises payment; the payee is the party named to receive it. Principal, date, rate, term, and payment instructions help translate that promise into a cash obligation.

In the day-count method used here, exclude the date the note is issued and include the maturity date. Count actual calendar days rather than pretending that each month has the same length. A 60-day note is not necessarily a two-calendar-month note.

The calendar determines how many days elapse; the interest convention determines the denominator used to convert those days to years. An actual/360 note still counts actual days even though interest uses a 360-day year. A note stated in calendar months instead follows its month-based due-date terms.

Before signing, identify any security, guarantor, late charges, or early-payment terms. These can change obligations without changing the printed principal. Weekend and holiday adjustments depend on the agreement and applicable rules; the classroom examples make no such adjustments.

Follow the note to maturity

  1. 1

    Issue

    April 10; principal $2,000

  2. 2

    Term

    60 days; interest $30

  3. 3

    Maturity

    June 9; amount due $2,030

Figure 11.1.V Follow the note to maturity. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • promissory note

    A written promise to repay a specific amount by a certain date.

  • maturity date

    The date a loan or note must be fully repaid.

  • bank discount

    Interest deducted from a loan in advance, so the borrower receives less than the face amount.

Key terms

Promissory note
A written promise to pay under stated terms.
Maker
The party promising to pay the note.
Payee
The party named to receive payment.
Maturity date
The date payment becomes due.
Collateral
Property pledged to secure an obligation.
Guarantor
A party who undertakes responsibility under a guarantee if its conditions are met.

Formulas & rules

  • Day-based interest

    I = P × r × (days ÷ year basis)

  • Maturity value

    M = P + I

  • Days remaining

    Remaining days = stated term − days already counted

Worked examples

Example 1Date and value of a note

Find the maturity date and value of the figure's April 10, 60-day, $2,000 note at 9%, actual/360.

Solution

  1. 1April 11–30 contributes 30 − 10 = 20 days.
  2. 2May contributes 31 days; 60 − 20 − 31 = 9 days remain in June.
  3. 3The maturity date is June 9; exclude April 10 and include June 9.
  4. 4I = 2,000 × 0.09 × 60 ÷ 360 = $30.00.
  5. 5M = 2,000 + 30 = $2,030.00.

Answer: Payment of $2,030.00 is due June 9.

Example 2A year-end note

A $1,460 note dated November 20 runs 45 days at 5%, actual/365. Find due date and maturity value; assume no holiday adjustment.

Solution

  1. 1November 21–30 contributes 10 days.
  2. 2December adds 31 days, leaving 45 − 10 − 31 = 4 days.
  3. 3Maturity is January 4 of the following year.
  4. 4I = 1,460 × 0.05 × 45 ÷ 365 = $9.00.
  5. 5M = 1,460 + 9 = $1,469.00.

Answer: The note matures January 4 for $1,469.00.

Practice exercises 11.1

  1. Find the due date of a 30-day note dated September 12.
  2. Find the due date of a 20-day note dated February 20 in a nonleap year.
  3. Find maturity value for $900 at 8% for 90 days, actual/360.
  4. A maker signs a note payable to an equipment seller. Who promises payment and who receives it?
  5. A note dated May 5 is due June 4. Count days and find interest on $1,200 at 6%, actual/360.

Recap quiz 11.1

1. Who makes the promise to pay?
2. A 10-day note dated April 25 matures:
3. $600 at 6% for 60 days, actual/360, has interest of:

Section 11.1 recap

  • Read the parties, rate, term, and payment provisions together.
  • Exclude the issue date and include the due date for these day-based notes.
Answer key with explanations: Section 11.1

Practice exercises

  1. September contributes 30 − 12 = 18 days; 30 − 18 = 12 days remain. The due date is October 12.
  2. February contributes 28 − 20 = 8 days; 20 − 8 = 12 days remain. Maturity is March 12.
  3. I = 900 × 0.08 × 90 ÷ 360 = $18.00; M = 900 + 18 = $918.00.
  4. The maker promises payment; the named equipment seller is the payee. These roles follow the promise, not the physical possession of the equipment.
  5. May 6–31 gives 26 days; June 1–4 gives 4, totaling 30. I = 1,200 × 0.06 × 30 ÷ 360 = $6.00.

Recap quiz

  1. Maker: The maker is the party promising payment.
  2. May 5: April 26–30 is 5 days; May 1–5 supplies the other 5.
  3. $6: 600 × 0.06 × 60 ÷ 360 = $6.
11.2

Bank Discount and Cash Proceeds

Learning objectives

After this section you will be able to:

  1. Distinguish interest-bearing notes from bank-discount notes.
  2. Calculate a discount and net proceeds.
  3. Measure cost relative to the cash actually received.

Real-life situation

Cash withheld before borrowing begins

A small vendor signs a non-interest-bearing discount note. Its face amount is the promised repayment; the lender subtracts the bank discount before handing over cash.

Cash withheld before borrowing begins

  • Face amount due: $2,000.00
  • Bank-discount rate: 6% annually; term: 90 days, actual/360
  • Discount: $30.00; proceeds: $1,970.00
Figure 11.2 Cash withheld before borrowing begins (hypothetical)

The concept

An interest-bearing note usually advances principal and adds interest at maturity. A bank-discount note instead subtracts its financing charge in advance. In the non-interest-bearing notes used here, face amount is also the maturity amount; no additional interest is added at maturity.

Bank discount is calculated on maturity value, not on usable cash. Multiply the maturity amount by the discount rate and time. Then subtract that discount to find proceeds. The borrower receives less than the amount promised for repayment.

A bank-discount rate understates the charge as a fraction of money actually received. A classroom simple annualized proceeds-based rate divides the discount by proceeds and by years. This indicator is not asserted to be a statutory APR.

A business can also sell an existing interest-bearing note before maturity. First determine that note's maturity value, then discount that maturity value for the remaining time. The two intervals and possibly the two rates serve different purposes.

Face amount is not cash received

Face amount$ 2,000
Bank discount$ 30
Cash proceeds$ 1,970

Bars share a zero baseline.

Figure 11.2.V Face amount is not cash received. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • principal

    The original amount of money borrowed or invested, before interest.

  • interest

    The cost of borrowing money, or the earnings on money saved or invested.

  • collateral

    Property a borrower promises to a lender if the loan is not repaid, such as a car.

Key terms

Face amount
The amount written on a note; for a non-interest-bearing discount note, the maturity obligation.
Bank discount
A financing charge deducted in advance from maturity value.
Discount rate
The annual rate applied to maturity value to calculate bank discount.
Proceeds
Cash received after discount is withheld.
Remaining term
Time from the discount date to the maturity date.

Formulas & rules

  • Bank discount

    D = M × d × t

  • Proceeds

    Proceeds = M − D

  • Proceeds-based indicator

    Annualized indicator = D ÷ proceeds ÷ t

Worked examples

Example 1A discounted note

Find discount, proceeds, and the annualized proceeds-based indicator for the figure's $2,000 note.

Solution

  1. 1t = 90 ÷ 360 = 0.25 year.
  2. 2D = 2,000 × 0.06 × 0.25 = $30.00.
  3. 3Proceeds = 2,000 − 30 = $1,970.00.
  4. 4Indicator = 30 ÷ 1,970 ÷ 0.25 = 0.0609137… .
  5. 5Express as approximately 6.09% annually.

Answer: The borrower receives $1,970.00 and owes $2,000.00; the indicator is about 6.09%.

Example 2Selling an interest-bearing note

A $3,000 note earns 8% simple interest over 120 days, actual/360. It is sold with 30 days remaining at a 6% bank-discount rate, actual/360. Find sale proceeds.

Solution

  1. 1Original interest = 3,000 × 0.08 × 120 ÷ 360 = $80.00.
  2. 2Maturity value = 3,000 + 80 = $3,080.00.
  3. 3Remaining time = 30 ÷ 360 year.
  4. 4Bank discount = 3,080 × 0.06 × 30 ÷ 360 = $15.40.
  5. 5Sale proceeds = 3,080 − 15.40 = $3,064.60.

Answer: The seller receives $3,064.60; the maker still owes $3,080.00 at maturity.

Practice exercises 11.2

  1. A $1,000 non-interest-bearing note is discounted at 8% for 90 days, actual/360. Find discount and proceeds.
  2. A maturity amount of $1,500 has $45 withheld. Find proceeds and the one-year proceeds-based indicator.
  3. Find proceeds for a $2,400 discount note at 5% for 60 days, actual/360.
  4. An existing note has maturity value $4,080 and 45 days remaining. Find bank discount at 4%, actual/360.
  5. A student discounts $2,000 principal instead of its $2,040 maturity value for 30 days at 6%, actual/360. Correct the proceeds.

Recap quiz 11.2

1. A discount note with face $500 and discount $10 provides:
2. Bank discount on an existing note is based on:
3. On a discount note, the proceeds-based annualized indicator is generally:

Section 11.2 recap

  • Bank discount is withheld up front and computed on maturity value.
  • Use only the remaining time when discounting an existing note.
Answer key with explanations: Section 11.2

Practice exercises

  1. D = 1,000 × 0.08 × 90 ÷ 360 = $20.00; proceeds = 1,000 − 20 = $980.00.
  2. Proceeds = 1,500 − 45 = $1,455.00; indicator = 45 ÷ 1,455 ÷ 1 ≈ 3.09%.
  3. D = 2,400 × 0.05 × 60 ÷ 360 = $20.00; proceeds = $2,380.00.
  4. Use maturity value: D = 4,080 × 0.04 × 45 ÷ 360 = $20.40.
  5. D = 2,040 × 0.06 × 30 ÷ 360 = $10.20; proceeds = 2,040 − 10.20 = $2,029.80. Discount applies to maturity value.

Recap quiz

  1. $490: Proceeds = 500 − 10 = $490.
  2. Maturity value: D = M × d × t uses maturity value M.
  3. Above the discount rate: The same charge is divided by proceeds smaller than maturity value, making this indicator larger.
11.3

Partial Payments and Obligation Records

Learning objectives

After this section you will be able to:

  1. Allocate partial payments under a stated interest-first rule.
  2. Calculate later interest on reduced principal.
  3. Separate contractual fees from principal and interest.

Real-life situation

A payment before maturity

A hypothetical note permits partial payments without penalty. Its stated allocation rule applies a payment first to accrued interest and then to principal, with actual/360 simple interest.

A payment before maturity

  • Opening principal: $1,000.00; annual rate: 12%
  • After 30 days: interest $10.00; payment $210.00
  • Principal reduction $200.00; new principal $800.00
  • After 30 more days: interest $8.00; payoff $808.00
Figure 11.3 A payment before maturity (hypothetical)

The concept

A payment record should distinguish principal, accrued interest, and fees. A payment is not automatically a principal reduction. Under this section's hypothetical interest-first rule, first calculate interest since the last transaction, then apply the payment to interest and use any remainder to reduce principal.

After principal changes, later simple interest is computed on the reduced outstanding principal. Do not continue charging on the original principal after a qualifying reduction, and do not charge a full original term again after every payment.

The examples assume each partial payment exceeds accrued interest. If a payment does not cover interest, the agreement must specify how unpaid interest is handled; do not silently capitalize it or declare the obligation satisfied. These examples do not establish a legal allocation rule.

Late fees and other obligations must follow the stated agreement and applicable rules. For classroom records, show a hypothetical fee separately and specify whether it earns interest. A clean record preserves dates, opening principal, elapsed time, interest, payment, and closing principal.

Record a partial payment

  1. 1

    Beginning principal

    $1,000

  2. 2

    Payment

    $210 → principal reduced to $800

  3. 3

    30 more days

    $8 interest → $808 payoff

Figure 11.3.V Record a partial payment. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • loan term

    How long a loan lasts before it must be fully repaid.

  • default

    Failing to repay a loan as agreed, which can harm credit and lead to collection.

  • payment terms

    The rules in an agreement about when a bill must be paid and any discounts for paying early.

Key terms

Accrued interest
Interest earned or owed since the last relevant date.
Partial payment
A payment smaller than the full outstanding obligation.
Interest-first allocation
A stated method applying payment to accrued interest before principal.
Principal reduction
The portion of a payment that decreases outstanding principal.
Payoff
The amount required to settle the obligation at a specified time.

Formulas & rules

  • Accrued interest

    I = outstanding principal × r × t

  • Principal reduction

    Reduction = payment − accrued interest

  • New balance

    New principal = old principal − reduction

  • Payoff

    Payoff = outstanding principal + accrued interest + unpaid separate fees

Worked examples

Example 1Two periods, one partial payment

Use the figure's $1,000 note at 12%: pay $210 after 30 days and settle 30 days later, actual/360.

Solution

  1. 1First-period interest = 1,000 × 0.12 × 30 ÷ 360 = $10.00.
  2. 2Payment toward principal = 210 − 10 = $200.00.
  3. 3New principal = 1,000 − 200 = $800.00.
  4. 4Second-period interest = 800 × 0.12 × 30 ÷ 360 = $8.00.
  5. 5Payoff = 800 + 8 = $808.00; total paid = 210 + 808 = $1,018.00.

Answer: The final payment is $808.00; total interest is $18.00.

Example 2A separately stated fee

A $600 note at 6%, actual/360, is settled after 60 days. A hypothetical $15 fee is due and earns no interest. Find payoff.

Solution

  1. 1t = 60 ÷ 360 = 1/6 year.
  2. 2Accrued interest = 600 × 0.06 × 1/6 = $6.00.
  3. 3Keep the non-interest-bearing fee separate: $15.00.
  4. 4Payoff = 600 + 6 + 15 = $621.00.

Answer: Payoff is $621.00, including $6.00 interest and a $15.00 fee.

Practice exercises 11.3

  1. On $1,200 at 9%, actual/360, pay $318 after 60 days. Find the new principal.
  2. The new principal is $900 at 9%. Find payoff 40 days later, actual/360.
  3. A $150 payment meets $12 accrued interest. How much reduces principal?
  4. A statement shows $450 principal, $7.50 interest, and a separate $10 non-interest-bearing fee. Find payoff.
  5. A $5 payment arrives when accrued interest is $8. Can the standard reduction formula be treated as a principal increase automatically?

Recap quiz 11.3

1. A $100 payment with $9 accrued interest reduces principal by:
2. After a valid principal reduction, later simple interest uses:
3. $300 principal, $4 interest, and $6 separate fee require payoff of:

Section 11.3 recap

  • Under the stated interest-first rule, only payment beyond accrued interest reduces principal.
  • Use a new time interval and the updated principal after each payment.
Answer key with explanations: Section 11.3

Practice exercises

  1. I = 1,200 × 0.09 × 60 ÷ 360 = $18; principal reduction = 318 − 18 = $300; new principal = $900.00.
  2. I = 900 × 0.09 × 40 ÷ 360 = $9.00; payoff = 900 + 9 = $909.00.
  3. Interest gets $12; principal receives 150 − 12 = $138.00.
  4. Payoff = 450 + 7.50 + 10 = $467.50; the fee is added once, not treated as principal.
  5. No. Interest exceeds payment by 8 − 5 = $3.00. Consult the agreement for unpaid-interest treatment; do not automatically capitalize the $3 or reduce principal.

Recap quiz

  1. $91: 100 − 9 = $91 reaches principal.
  2. Reduced outstanding principal: The new principal is the base for the next interval.
  3. $310: 300 + 4 + 6 = $310.

Chapter 11 Organizer and Review

Chapter Organizer

Every section at a glance: key formulas, key terms, and the main idea.

  • 11.1 Reading Notes and Finding Maturity Dates

    Key formulas

    • Day-based interest: I = P × r × (days ÷ year basis)
    • Maturity value: M = P + I
    • Days remaining: Remaining days = stated term − days already counted

    Key terms

    Promissory note, Maker, Payee, Maturity date, Collateral, Guarantor

    Remember

    Read the parties, rate, term, and payment provisions together.

  • 11.2 Bank Discount and Cash Proceeds

    Key formulas

    • Bank discount: D = M × d × t
    • Proceeds: Proceeds = M − D
    • Proceeds-based indicator: Annualized indicator = D ÷ proceeds ÷ t

    Key terms

    Face amount, Bank discount, Discount rate, Proceeds, Remaining term

    Remember

    Bank discount is withheld up front and computed on maturity value.

  • 11.3 Partial Payments and Obligation Records

    Key formulas

    • Accrued interest: I = outstanding principal × r × t
    • Principal reduction: Reduction = payment − accrued interest
    • New balance: New principal = old principal − reduction
    • Payoff: Payoff = outstanding principal + accrued interest + unpaid separate fees

    Key terms

    Accrued interest, Partial payment, Interest-first allocation, Principal reduction, Payoff

    Remember

    Under the stated interest-first rule, only payment beyond accrued interest reduces principal.

Cumulative Review

Mixed practice from this chapter and the two chapters before it.

  1. Section 11.1

    A note dated May 5 is due June 4. Count days and find interest on $1,200 at 6%, actual/360.

    Show answer

    May 6–31 gives 26 days; June 1–4 gives 4, totaling 30. I = 1,200 × 0.06 × 30 ÷ 360 = $6.00.

  2. Section 11.2

    A student discounts $2,000 principal instead of its $2,040 maturity value for 30 days at 6%, actual/360. Correct the proceeds.

    Show answer

    D = 2,040 × 0.06 × 30 ÷ 360 = $10.20; proceeds = 2,040 − 10.20 = $2,029.80. Discount applies to maturity value.

  3. Section 11.3

    A $5 payment arrives when accrued interest is $8. Can the standard reduction formula be treated as a principal increase automatically?

    Show answer

    No. Interest exceeds payment by 8 − 5 = $3.00. Consult the agreement for unpaid-interest treatment; do not automatically capitalize the $3 or reduce principal.

  4. Review of Section 9.3

    Gross is $450 and total employee deductions are $65. Find net pay.

    Show answer

    450 − 65 = $385.00.

  5. Review of Section 10.3

    A $700 face loan withholds $25 and requires $735 at maturity. Find proceeds and cost.

    Show answer

    Proceeds = 700 − 25 = $675.00; cost = 735 − 675 = $60.00.

All prices, stores, people, and accounts in this chapter are hypothetical and for teaching only. Product references are generic categories; no brand endorses or is endorsed by this textbook.

Chapter 10Chapter 12