Your Money and and Your Math Chapter 13

Interest, Taxes, and Discounts 13.1

Simple Interest

TIME Time must be measured in years or parts of years There are two types of simple interest based on time: a). Ordinary interest months in a year days in each month in a year b). Exact interest months in a year 2. exact number of days in the month days in a year (ignore leap year)

The formula for calculating simple interest I on a principal P at the rate r for t years is I = Prt Final Amount The final amount A is given as A = P + I. Simple Interest

Find the simple interest. PrincipalRateTime 1.$20009%3 years 2.$250010%3 months 3. $ % 95 days (ordinary) 4. $1200 4% 112 days (exact) Examples

1.I = Prt = $2000*.09*3 = $ I = Prt = $2500*0.1*3/12 = $ I = Prt = $1500*0.025*95/360 = $ I = Prt = $1200*0.04*112/365 = $14.73

Taxes

“ There is nothing certain but death and taxes.” Here is a problem that “it is certain” you can do. The sales tax in Alabama is 4%. Beto Frias bought a refrigerator priced at $666. a. What was the sales tax on this item? b. What was the total price of the purchase? Taxes a.Sales Tax = $666*.04 = $26.64 b.Total Price = $ $26.64 = $692.64

Discounts

The consumer has to pay interest or taxes. But there is some hope! Sometimes you obtain a discount on certain purchases. A Sealy mattress sells regularly for $900. It is offered on sale at 25% off. a. What is the amount of the discount? b. What is the price after the discount? c. If the sales tax is 6%, what is the total price of the mattress after the discount and including the sales tax? Discounts

b.Price = $900 - $225 = $675 a.Discount = $900*0.25 = $225 c.Sales Tax = $675*0. 06 = $40.50 Final Total = $675 + $40.50 = $715.50

Compound Interest

where and A is the future (maturity) value; P is the principal; is the present (today) value r is the annual interest rate; m is the number of compounding periods per year; t is the number of years; n is the number of compounding periods; i is the interest rate per period. Compound Amount When interest is compounded, the interest is calculated not only on the original principal but also on the earned interest:

Future Value for Compound Interest If P dollars are deposited at an annual interest rate r, compounded m times a year, and the money is left on deposit for n periods, the future value(or final amount) A n is Compound Interest

Example Suppose you invest $1000 at 6% compounded quarterly for 1 year. How much money would you have?

Future Value for Continuously Compounded Interest If P dollars are deposited and earn continuously compounded interest at an annual rate r for t years, then the future value A n is Compound Interest

Find the compound amount when $2000 is compounded continuously at 8% for 6 months. How much interest will be earned? Example

Formula for APY (Effective Rate) APY = Compound Interest k the number of compounding periods per year, r the rate for continuous compounding

Find the APY (effective annual rate) a.6% compounded monthly b.8% compounded continuously Examples

Present Value Compound Interest: Simple Interest: Continuous Interest:

Examples a.Larry owes Tom $1500 in eight months. Find the amount Larry would pay Tom today if they agree money is worth 7% simple interest. b.A small company has agreed to pay $40,000 in 3 years to settle a lawsuit. How much must they invest now in an account paying 6% compounded quarterly to have that amount when it is due? c.How much would the company have to invest today if they could receive 5.5% compounded continuously?

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