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Thinking Mathematically

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Presentation on theme: "Thinking Mathematically"— Presentation transcript:

1 Thinking Mathematically
Consumer Mathematics and Financial Management 8.3 Compound Interest

2 Calculating the Amount in an Account for Compound Interest Paid Once a Year
If p dollars are deposited at a rate r, in decimal form, subject to compound interest, then the amount, A, of money in the account after t years is given by: A = P(1+r)t. The amount A is called the accounts future value and the principal P is called its present value.

3 Example -- Compound Interest
Exercise Set 8.3 #1 P = $10,000, r = 4%, t = 2 years. What is the future value if the interest is compounded annually? How much interest is earned?

4 Calculating the Amount in an Account for Compound Interest Paid n Times a Year
If p dollars are deposited at rate r, in decimal form, subject to compound interest paid n times per year, then the amount, A, of money in the account after t years is given by: A is the account’s future value and the principal P is its present value.

5 Example – Compound Interest
Exercise Set 8.3 #5 P = $9500, r = 6%, t = 5 years. What is the future value if interest is compounded quarterly? How much interest is earned?

6 Calculating Present Value
If A dollars are to be accumulated in t years in an account that pays rate r compounded n times per year, then the present value, P, that needs to be invested now is given by

7 Example – Present Value
Exercise Set 8.3 #19 An account earns 9.5% compounded monthly. How much must be invested in order to have $10,000 in three years?

8 Effective Annual Yield
The effective annual yield, or the effective rate, is the simple interest rate that produces the same amount of money in an account at the end of one year as there is when the account is subjected to compound interest at a stated rate.

9 Calculating Effective Annual Yield
Suppose that an investment has a nominal interest rate, r, in decimal form, and pays compound interest n times per year. The investment’s effective annual yield, Y, is given by

10 Example – Effective Annual Yield
Exercise Set 8.3 #25 A passbook savings account has a rate of 6% compounded monthly. What is the effective annual yield?

11 Thinking Mathematically
Consumer Mathematics and Financial Management 8.3 Compound Interest


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