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
“ 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
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
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
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?