Finance & Binomial Theorem (Lesson).notebook

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UNIT #8: Finance & Binomial Theorem

Learning Goal: I will learn how to calculate the simple and compound interest of a monetary amount.

Simple and Compound InterestSimple Interest

Simple interest is interest paid on an investment each investment period (e.g. month, year). The interest is not rolled back into the original investment.

I = PrtI - dollars is the interest earned

r - is the annual interest rate

t - is the time in years

Example 1:a) How much interest would be earned on a $1000 GIC at 5% for 1 year?

I = Prt 1000 (0.05) (1) = $50

b) What amount will the investor have after 10 years?

Interest earned: 1000 (0.05) (10) = $500 Total accumulated: $500 + $1000 (original investment) = $1500

Compound InterestWith compound interest, the interest is reinvested at regular intervals (called the compounding period). Interest for the next period is paid on the original investment and the interest that accrued in the previous compounding period(s).

A = P(1 + i)n

A - amount at the end of the investment periodP - principal or original investmenti - interest rate over the compounding periodn - number of compounding periods

Finance & Binomial Theorem (Lesson).notebook

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Example 2: a) How much will a $1000 investment be worth at the end of 10 years with an interest of 5% compounded annually:

A = P(1 + i)n

= 1000(1 + 0.05)10

= 1628.89

b) How much interest was paid? Amount - Original Investment = 1628.89 - 1000 = $628.89.

c) How much more money does the investor make with compound interest than with simple interest? $1628.89 - $1500 = $128.89

Example 3: Calculate the interest paid if interest is compounded semi-annually.

P = 1000i = 0.05 / 2 = 0.025n = 10 x 2 = 20

A = P(1 + i)n

= 1000(1 + 0.025)20

= 1638.61

UNIT 8: Finance & Binomial TheoremSimple and Compound Interest

Learning Goal: I will learn how to calculate the simple and compound interest of a monetary amount.

Practice Work

Success Criteria:To be successful, I must be able to...• understand the difference between simple interest and compound interest• Calculate simple interest using I = Prt• Calculate the amount of an investment that has compounded interest using A = P(1 + i)n

p. 498 #1p. 508 #1, 2, 4a, c, 11-14, 19-20