MBF3C Lesson #2: Simple & Compound Interest PERSONAL FINANCE MBF3C Lesson #2: Simple & Compound Interest

Learning Goals To state the difference between simple and compound interest To identify simple interest as linear relation and compound interest as an exponential relation 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

I = P r t IMPLE INTEREST FORMULA Annual interest rate Interest paid Time (in years) 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 Principal (Amount of money invested or borrowed)

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)

enter in formula as a decimal 100 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. enter in formula as a decimal I = P r t 10 = (200)(0.04)T 1.25 yrs = T Typically 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).

COMPOUND INTEREST …is calculated on the accumulated value of the investment, which includes the principal and the accumulated Albert Einstein once said that compound interest was the most powerful force of all time.  He was a pretty smart guy! Compound interest is really a math concept that shows the power of making interest on not just your principal but also interest.  If you have $1000 and you make 5% interest, after the first year, you will have $1050.  If you let the interest compound, the second year you will not make $50 of interest again but rather $52.50 of interest because you are making 5% off the $1050.  In other words, you made and extra $2.50 of interest on the $50 of interest from the previous year.  After the second year you will have $1102.50.  In the third year, you will have $1157.63

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.

TOMORROW WE WILL GO OVER COMPOUND INTEREST AND USE A FORMULA TO DO SO! 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 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 the year using the formula I = Prt. Years Simple Interest ($) Amount ($) 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 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 Start of Year ($) Compound Interest ($) Amount at the end of year ($) 1000 70 1070 1 2 3 4 5 6 7 8 9 10 11 12

3. Look at the entries in the tables 3. Look at the entries in the tables. Compare the amounts for simple interest to the amounts for compound interest. Explain the diff 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