Single Payment Loan-BM

• Business Math
• Secondary Education

Brainstorm

Where can you find the funds for starting up the business?

Chapter8.1:Single Payment Loans

• Describe a single-payment loan
• Compute the maturity value and interest rate of a single payment loan
• Evaluate the due date for loan payment

Chapter 8.1: Single Payment Loans

Pages 305-307

Single payment loan

A single-payment loan is a loan that you repay with one payment after a specified period of time. 

A business may be short of funds and need to borrow money to meet its payroll or pay for inventory and supplies.

Definitions

• A promissory note is a written promise to pay a certain sum of money on a specific date in the future.
• The maturity value of the loan is the total amount you must repay. It includes both the principal and the interest owed.
• A loan’s term is the amount of time for which the loan is granted.

1. Ordinary interest is based on a 360-day year.

2. Exact interest is based on a 365-day year.

What is the significance of a single payment loan?

What is a written promise to pay a certain sum of money on a specific date in the future?

1. Cheque
2. Promissory note
3. Invoice
4. Memo

What is the total amount you must repay?

1. Promissory note
2. Single payment
3. Maturity Value
4. Multiple payments

Formula

Interest = Principal × Rate × Time

Ordinary Interest = Principal × Rate × Time/360

Exact Interest = Principal × Rate × Time/365

Maturity Value = Principal + Interest

Example 1

Anita Sloane’s bank granted her a single-payment loan of $7,200 for 91 days to pay for new merchandise for her candle shop. Determine the maturity value of the loan if the rate is (a) 6% ordinary interest or (b) 6% exact interest.

Solution

Step 1: Find the ordinary interest owed.

Ordinary Interest = Principal × Rate × Time/360

$109.20 = $7,200.00 × 0.06 × 91/360

Step 2: Find the maturity value with ordinary interest.

Maturity Value = Principal + Interest

$7,309.20 = $7,200.00 + $109.20

Step 3: Find the exact interest owed.

Principal × Rate × Time/365

$7,200.00 × 0.06 × 91/365

= $107.704 = $107.70 Exact Interest

Step 4: Find the maturity value with exact interest.

Maturity Value = Principal + Interest

$7,307.70 = $7,200.00 + $107.70

Compute the (a) interest and (b) maturity value for each loan.
1. Parker Logan purchased a new surfboard costing $600 and financed it at 9% ordinary interest for 90 days.

Give the steps of calculating the interest and maturity value of a loan.

Example 2

Claudia Valdez took out a single-payment loan for $1,500.00 at 7.8% ordinary interest to pay her federal income tax bill. If the loan’s maturity value is $1,529.25, when would Claudia have to pay back the loan if she took it out on March 1?

Solution

Step 1: Find the interest

Maturity Value = Principal + Interest or Interest = Maturity Value – Principal

Interest = $1,529.25 – $1,500.00 = $29.25

Step 2: Find the time of the loan in days, t.

Ordinary Interest = Principal × Rate × t/360

$29.25 = $1,500.00 × 0.078 × t/360

$10,530 = $117t

90 = t

Claudia would have to pay back the loan in 90 days.

Step 3: Find the due date. Use the Elapsed Time Table on page A10. March 1 is the day

60 + 90 days = day 150, which is May 30.

How long would it take a construction loan for $548,048 to earn interest of $50,000 at 9% exact interest?

Let t = How long it would take in days

$50,000 = $548,048× 0.09 ×t/365

$18,250,000 =$49,324.32t

370 = t

How can you calculate the time to pay back?

Give the main points of the lesson.