PERSONAL FINANCE

MBF3C

Lesson #3: Compound Interest

Some notes about simple vs. compound Interest

Simple interest is a linear relation. Interest is only earned on the original principle.

Compound interest is exponential. Interest is earned not only on the original principle but also on the interest which has been earned so far.

 The difference between simple and compound interest is very small over a short period of time. However, unlike simple interest, if you earn compound interest, the amount of interest continues to increase over time. Over a long period of time, the interest earned in compound interest is much larger than the interest earned with simple interest.

The time interval between the occasions at which interest is added to the account is called the compounding period . The chart below describes some of the common compounding periods:

Compounding Period

Descriptive Adverb

Fraction of one year

# of times

1 day daily 1/365 (ignoring leap years, which have

366 days)

365

1 month monthly 1/12 123 months quarterly 1/4 46 months semiannually 1/2 2

1 year annually 1 1

Rather than using a table or a graph to see how the value of an investment grows, you can use a formula.

niPA 1

P is the principal, or initial value.A is the accumulated amount or future value.i is the interest rate per compounding period.n is the number of compounding periods.

niPA 1

The table shows how to convert the yearly interest rate and term for various compounding periods.

*continued on next slide

% per year compoundedNumber of compound

periods per yearValue for i Value for n

Annually 1

Semi-annually 2

Every six months 2

Quarterly 4

Every three months 4

Monthly 12

Weekly 52

Daily 365

compounds

rate

number of times per year that

interest in compounded

WHAT EXACTLY DOES THE “i” MEAN?

Interest rate as a decimal

Annually Once a yearSemi-annually 2 timesa year

Quarterly 4 times a yearMonthly 12 times a year

Bi-weekly 26 times a yearWeekly 52 times a yearDaily 365 times a year

WHAT EXACTLY DOES THE “n” MEAN?

Number of times per year that interest is compounded per year

Number of Yearsx

Annually Once a yearSemi-annually 2 timesa year

Quarterly 4 times a yearMonthly 12 times a year

Bi-weekly 26 times a yearWeekly 52 times a yearDaily 365 times a year

Example:Interest Compounded Semi-Annually

Determine how much money you will have if $500 is invested for six years, at 4% per year, compounded semi-annually.

Solution

Interest is compounded semi-annually, meaning twice a year, for six years. There are 2 × 6, or 12, compounding periods. This can be illustrated on a timeline.

Determine how much money you will have if $500 is invested for six years, at 4% per year, compounded semi-annually.

i = 0.04 ÷ 2

= 0.02

n = 6 × 2

= 12

P = 500

A= 500(1+0.02)12

= 634.12 After six years, you will have $634.12.

niPA 1

Example:Interest Compounded Monthly

Alice borrowed $5000 to start a small business. The interest rate on the loan was 9% per year, compounded monthly. She is expected to repay the loan in full after four years.a) How much must Alice repay?

b) How much of the amount Alice repays will be interest?

A) How much must Alice repay?

Alice borrowed $5000 to start a small business. The interest rate on the loan was 9% per year, compounded monthly. She is expected to repay the loan in full after four years.

Interest is compounded monthly, meaning 12 times a year, for four years. There are 12 × 4, or 48, compounding periods.

Alice borrowed $5000 to start a small business. The interest rate on the loan was 9% per year, compounded monthly. She is expected to repay the loan in full after four years.

i = 0.09 ÷ 12

= 0.0075

n = 4 × 12

= 48

P = 5000

A= 5000(1+0.0075)48

= 7157.03 Alice must repay $7157.03 after four years

niPA 1

B) How much of the amount Alice repays will be interest?

Calculate the total interest by subtracting the principal from the amount.

7157.03 - 5000 = 2157.03

Therefore, Alice will pay $2157.03 in interest.

Key Concepts (p. 432)

Compound interest can be accumulated at various intervals, such as annually, semi-annually, quarterly, and monthly.

The compound interest formula A = P(1 + i)n can be used to calculate the future value, or amount

– A is the future value or accumulated amount of an investment or loan.

– P is the principal.

– i is the interest rate, in decimal form, per interest period.

– n is the number of compounding periods.

IN-CLASS & HOMEWORK

Page 432, # 1ace, 2bc, 3bd, 4, 5, 7, 8abcd

SUCCESS CRITERIA FOR THIS LESSON:

I can ____ Calculate the number of compound periods (n)

and periodic interest rate (i) ____ Calculate the future amount or value of an

investment using compound interest compounded over different periods

____ Calculate the interest earned on an investment