Lecture Notes on Chapter 13-15 - Modern Business Mathematics | MTH 130, Study notes of Mathematics

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MTH 130

M0DERN BUSINESS

MATHEMATICS

UNIT 4

CHAPTERS 13 - 15

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

13.1 – Introduction and Terminology

Who’s the borrower?

Who’s the lender?

What is the principal?

What is interest?

Formula:

1. Find the missing quantity

Principal Interest Amount

a. $ 2,600 $ 2,

b. $18,000 $19,

c. $80,000 $8,

2. The interest on a loan of $2500 for 3 years at 7.5% is $562.50. Find the principal, interest, rate, time and amount.

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

Principal Rate Time Interest Amount

b. $6,000 2 years $1,

c. 4 years $2,000 $12,

d. $7,000 10% / year $8,

2. An investment of $5000 at an annual rate of 8.5% for 36 months. Find the interest and total amount.

Exact Time versus Approximate Time

a. Exact Time:

b. Approximate Time:

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

Examples:

3. From May 18 to November 29 of the same year. Find the exact and approximate time.
4. From March 15 to December 12 of the same year. Find the exact time using table 13.

Banker’s Rule

Popular rule that will result with the _____________ amount of interest for the lender.

Banker’s Rule = _______________________________

Examples:

5. Find the interest and total amount to be repaid for a loan of $1000 at 8.5% per year from January 12 to September 12 of the same year, which is not a leap year.

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

Examples:

8. An investment at 7.75% for 30 months earned $620 interest. What was the original investment?
9. The total amount repaid on the loan was $13,560. If the loan was 2 years at 10% per year, what was the original value of the loan
10. Jack Barrett bought a piece of property for $15,000. He agreed to pay $5000 down and $2500 plus 8.5% interest on the unpaid balance at the end of each year for 4 years. What will be the total cost of the property?

Interest Amount Paid Balance

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

13.3 – Notes

Also called _________________________ notes

Written ___________________ on the part of the maker to __________ a certain sum of

money to another person (the _______________) on a certain date.

Notes are normally written for loans that are __________ than a year

Requires ________________________ such as ____________, _____________________,

_______________)

There are two types of notes:

• Simple Interest Notes
• Bank Discount Notes.

Simple Interest Notes

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

Bank Discount Notes

Examples:

6. What are the interest deducted in advance and the proceeds for a $3500 bank discount note with an annual interest rate of 11% and a term of 9 months
7. Determine the interest deducted in advance and the proceeds for a $1500 bank discount note at 8.75% from May 9 to August 7 of the same year.

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

8. Determine the maturity date, the interest deducted in advance, and the proceeds for a $2800 bank discount note at 10% written on July 10 for 4 months.
9. Compare a simple interest note for $10,000 at 9.5% for 1 year to a bank discount note for $10,000 at 9.5% for 1 year.
10. For a $6000 bank discount note at 11% for 1 year, what is the interest rate on the actual sum received?

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

Interest Rate per Period

Interest rate per period = _______________________________ = i

Examples :

• Semiannually means _______________times a year
• Quarterly means__________________ times a year
• Monthly means ___________________ times a year
• Biweekly means __________________ times a year
• Weekly means___________________ times a year

Examples: For numbers 1 – 2, find the compound amount and compound interest

Principal Rate Term Interest Period

1. $1000 6% 2 years Annually
2. $4000 7.5% 1 year Semiannually

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

3. What is the maturity value after 2 ½ years, of a loan of $2,000 made at 10% compounded semiannually?

As you can see, as the number of periods increased, the process become more and more tedious and from now on we will use the following formula:

(1 )

n A = P + i

Where… A =

P =

i =

n =

Example:

4. Stated Rate Interest Period Term i n

7% Monthly 36

5 years 2% 20

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

7. Otto Bergman deposits $2,500 in his savings account that pays 5% compounded monthly. After 2 years Otto withdraws $500 and leaves the rest of his money in the bank for another four years. How much is in his account at the end?
8. Mike O’Leary opens a savings account with a deposit of $4,000. Six months later he withdrew $1,000 and two years later he deposited $500. If the bank pays 7% compounded semiannually, what is Mike’s balance at the end of 3 years?

The principal is often called the present value.

If we rearrange our formula (1^ )

n A = P + i in order to isolate P we will find:

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

Find the present value if…

Amount Annual Rate Interest Period Term

9. $500 8% Annually 6 years
10. $500 8% Quarterly 2 years
11. Ramiro Rodriquez would like to establish a fund of $40,000 to help pay for his son’s college education ten years from now. If a bank has a 10 year CD that will pay 9% compounded quarterly, how much must Ramiro deposit in that account today?

Brigitte Martineau UNIT 5 – Chapters 13, 14 and 15

Examples

1. Betty and Al Barber decided to open a savings account in order to save for their retirement. They decided to deposit $5000 in their account at the end of every year for the next 25 years. How much will they have in their account at that time, if the interest rate is 7% compounded yearly?
2. Betty and Al Barber decided to open a savings account in order to save for their retirement. They decided to deposit $500 in their account at the end of every 3 months for the next 25 years. How much will they have in their account at that time, if the interest rate is 7% compounded quarterly?
3. To save for a new car, Walt Forrest decided to deposit $250 in a savings account at the end of each month for 2 years. How much will Walt have saved if the interest rate is 6% compounded monthly?