Chapter 10: The Mathematics of Money

Size: px

Start display at page:

Download "Chapter 10: The Mathematics of Money"

Malcolm Strickland
5 years ago
Views:

1 Chapter 10: The Mathematics of Money Percent Increases and Decreases If a shirt is marked down 20% and it now costs $32, how much was it originally? Simple Interest If you invest a principle of $5000 and a bond pays 2% annual simple interest, how much does it pay you each year? Compound Interest If you invest a principle of $5000 in a bank account that offers 2% annual compound interest, how much is the account worth after 10 years? Fixed Deferred Annuity If you invest $500 each year into an account that offers 6% annual (compound) interest, how much will the account be worth in 10 years? Percent Increases and Decreases Q = (Original) Quantity x% is percent increase or decrease Book uses "I" for result of an increase and "D" for the result of a decrease. Let's use "A" for the amount (after the change) (it might be more or less than Q, depending on the problem) If the population of a town is 25,000 and it increases by 10%, what is the new population.

2 If the population of a town is 25,000 and it increases by 10%, what is the new population.

3 If a shirt costs $32 and is marked down 25%, how much will it cost? If a shirt is marked down 20% and it now costs $32, how much was it originally? Suppose a store offers a "No Tax" sale. They say that since sales tax is 7%, they will give you a 7% discount, so that you won't pay any taxes. Does that really work? Does it come out to the original price?

4 Simple Interest If you invest a principle of $5000 and a bond pays 2% annual simple interest, how much does it pay you each year? In simple interest, the money you earn is NOT added back into the account. Recursive Formula vs. Explicit Formula Suppose you have $1000 invested. A bond pays out 4% annual interest (not reinvested). A0 = Amount after Zero years A1 = Amount after ONE year A2 = Amount after TWO years A3 = Amount after Three years AN = Amount after N years AN+1 = Amount after N+1 years

5 Compound Interest If you invest a principle of $5000 in a bank account that offers 2% annual compound interest, how much is the account worth after 10 years? In Compound Interest, the interest you earn is put back into the account. So you earn "interest on the interest" A 0 = Amount after Zero years A 1 = Amount after ONE year A 2 = Amount after TWO years A 3 = Amount after Three years A N = Amount after N years Present Value vs. Future Value If you invest a certain amount in a bank account that offers 7% annual compound interest, suppose its future value is $20,000 after 10 years? What is its present value?

6 Compounded Quarterly Start You want to invest $1000. Suppose two banks promises 8% annual interest. However Bank B will compound the interest "quarterly" i.e. four times per year. What's the difference? Bank A Bank B Start After 3 months After 1 year After 6 months After 9 months After 1 year

7 Compounded Quarterly You want to invest $1000. Suppose two banks promises 8% annual interest. However Bank B will compound the interest "quarterly" i.e. four times per year. What's the difference? Bank A Bank B Start After 1 year After 1 year After 2 years After 15 months After 18 months After 21 months After 2 years Compounded Quarterly You want to invest $1000. Suppose two banks promises 8% annual interest. However Bank B will compound the interest "quarterly" i.e. four times per year. What's the difference? Bank A Bank B After " t " years After " t " years

8 Compounded Monthly You want to invest $1000. Suppose two banks promises 8% annual interest. However Bank C will compound the interest "monthly" i.e. twelve times per year. What's the difference? Start Bank A Bank B Start After 1 month After 2 months After 6 months After 1 year After 1 year Effective Annual Interest Rate. By what rate does your investment grow when the bank offers 8% annual interest compounded QUARTERLY? By what rate does your investment grow when the bank offers 8% annual interest compounded MONTHLY?

General Compounding Formula F = Future value of money P = principle (original amount invested) r% interest compounded n times per year for t years General Exponential Formula (Version 2 in Book) p =

9 General Compounding Formula F = Future value of money P = principle (original amount invested) r% interest compounded n times per year for t years General Exponential Formula (Version 2 in Book) p = periodic interest rate Total of T Compounding periods Continuous Compounding Formula What happens when a bank compounds the interest weekly or daily or hourly or "secondly"... Do you can huge amounts of money? Suppose the annual interest rate is 10% and you invest $1000. Annual monthly Daily Hourly (8760 hours in a year)

10 Continuous Compounding Formula What happens when a bank compounds the interest weekly or daily or hourly or "secondly"... Do you can huge amounts of money? Suppose the annual interest rate is 10% and you invest $1000.

11 Chapter 10 Homework Problems from the Book

Math116Chap10MathOfMoneyPart2Done.notebook March 01, 2012

Math116Chap10MathOfMoneyPart2Done.notebook March 01, 2012 Chapter 10: The Mathematics of Money PART 2 Percent Increases and Decreases If a shirt is marked down 20% and it now costs $32, how much was it originally? Simple Interest If you invest a principle of