# Your Money and and Your Math Chapter 13. Interest, Taxes, and Discounts 13.1.

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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 1. 12 months in a year 2. 30 days in each month 3. 360 in a year b). Exact interest 1. 12 months in a year 2. exact number of days in the month 3. 365 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. \$1500 2.5% 95 days (ordinary) 4. \$1200 4% 112 days (exact) Examples

1.I = Prt = \$2000*.09*3 = \$540.00 2.I = Prt = \$2500*0.1*3/12 = \$62.50 3.I = Prt = \$1500*0.025*95/360 = \$9.90 4.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 = \$666.00 + \$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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