PERSONAL FINANCE

MBF3C

Lesson #2: Simple & Compound Interest

Learning Goals

1.To state the difference between simple and compound interest

2.To identify simple interest as linear relation and compound interest as an exponential relation

3.To solve word problems involving simple and compound interest

INTRODUCTION

Banks pay you interest for the use of your money. When you deposit money in a bank account, the bank reinvests your money to make a profit.

REMEMBER:

INTEREST

…a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets.

SIMPLE

AND

COMPOUND INTEREST

Since this section involves what can happen to your money, it should be of

INTEREST to you!

SIMPLE INTEREST

Simple interest is calculated on the initial value invested (principal ), P, at an annual interest rate, r, expressed as a decimal for a period of time, t. The interest is added to the principal at the end of the period.

Interest, I = Prt

Annual interest rate

IMPLE INTEREST FORMULA

Interest paid

Principal(Amount of money invested or borrowed)

Time (in years)I = P r t

Parts

Simple interest • the money paid on a loan or investment a percent of the principal

Principal • the value of the initial investment or loan

Amount • the final or future value of an investment, including the principal and the accumulated Interest

SIMPLE INTEREST

Simple interest is calculated on the initial value invested ( principal ), P, at an annual interest rate, r, expressed as a decimal for a period of time, t. The interest is added to the principal at the end of the period.

Interest, I = Prt Amount , A = P + Prt Or in factored form, A = P(1 + rt)

If you invested $200.00 in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $10.00.

10 = (200)(0.04)T

1.25 yrs = TTypically interest is NOT simple interest but is paid semi-annually (twice a year), quarterly (4 times per year), monthly (12 times per year), or even daily (365 times per year).

enter in formula as a decimal I = P r t

100

COMPOUND INTEREST

…is calculated on the accumulated value of the investment, which includes the principal and the accumulated

INVESTIGATION (Page 422)

Compare the growth of a $1000 investment at 7% per year, simple interest, with another $1000 investment at 7% per year, compounded annually.

Rather than using a table or a graph to see how the value of an investment

grows, you can use a formula.

TOMORROW WE WILL GO OVER COMPOUND INTEREST AND USE A FORMULA TO DO SO!

1. Set up a table as shown. Complete the table for 0 to 12 years.Calculate the simple interest on the amount at the start of theyear using the formula I = Prt.

Years Simple Interest ($) Amount ($)

0

1

2

3

4

5

6

7

8

9

10

11

12

2. Set up a chart as shown. Complete the chart for 0 to 12 years.Calculate the interest, at 7% per year, on the previous value (amount)and add it to the amount before calculating interest for the next year.

Years Amount at Startof Year ($)

Compound Interest($)

Amount at the end of year ($)

0 1000 70 1070

1 1070

2

3

4

5

6

7

8

9

10

11

12

3. Look at the entries in the tables. Compare the amounts for simpleinterest to the amounts for compound interest. Explain thediff erences in the growth for the two amounts.

4. Sketch a scatter plot of both sets of data on the same set of axes.

5. How do the graphs compare? Explain the differences in the graphs.

6. Reflect Describe how compound interest grows relative to simple interest.

7. Identify the type of growth (linear, quadratic, or exponential) demonstrated by simple interest and by compound interest. Justify your choices.

The growth factor is 1 + i, where i is the interest rate per compounding period , n.

Growth factor: the number that is multiplied by the principal when calculating its accumulated value

Compounding period: the length of time for which interest is calculated before being accumulated

Compare Simple and Compound Interest(page 426)

EXAMPLE:

Larry wants to invest $700 for five years. Compare the growth of his investment at 4% per year, simple interest, to the same investment at 4% per year, compounded annually.

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

formula.

TOMORROW WE WILL GO OVER COMPOUND INTEREST AND A FORMULA FOR FINDING IT!

IN-CLASS & HOMEWORK

PAGE 428-429, Q 1 - 12