Computing Simple Interest Earned Dianna deposits $725 into a - - PowerPoint PPT Presentation

DAY 86 – INTRODUCE THE POWER

OF INTEREST

VOCABULARY

Interest: The amount of money that you pay to borrow money or the amount of money that you earn on a deposit Annual Interest Rate: The percent of interest that you pay for money borrowed, or earn for money deposited. Simple interest formula: I = Prt where I is the interest earned, P is the principal or the amount of money that you start out with, r is the annual interest rate as a decimal, and t is the time in years. Balance: The sum of the principal P and the interest Prt.

EXAMPLE 1

Computing Simple Interest Earned

Dianna deposits $725 into a savings account that pays 2.3% simple annual

• interest. How much interest will Dianna

earn after 18 months?

SOLUTION

In the simple interest formula, time is measured in years. Write 18 months as , or 1.5 years. Write the annual interest rate as a decimal.

1 2 1 8

Multiply 01 . 25 $ for 1.5 & , for ,0.023 for $725 Substitute ) 5 . 1 )( 023 . )( 725 ( interest simple for formula the Use Pr    I t r P I t I

ANSWER Diana will earn $25.01 in interest

EXAMPLE 2

FINDING THE BALANCE

You deposit $300 in a savings account that pays 4% simple annual interest. Find your account balance after 9 months.

SOLUTION

Write 9 months year , or 0.75 year.

1 2 9

Add. 309 Multiply. 9 300 . for 0.75 & , for 0.04 P, for $300 Substitute ) 75 . )( 04 . )( 300 ( 300 formula balance the Write Pr        t r t P A

ANSWER Your account balance after 9 months is $309

VOCABULARY

Compound interest: Interest that is earned on both the principal and any interest that has been earned previously. Compound interest formula: A = P(1 + r)t where A represents the amount of money in the account at the end of the time period, P is the principal, r is the annual interest rate, and t is the time in years. Balance: The sum of the principal and the interest

EXAMPLE 1

Computing Compound Interest using Simple Interest

Simon deposits $400 in an account that pays 3% interest compounded annually. What is the balance of Simon’s account at the end of 2 years?

SOLUTION

Step 1 Find the balance at the end of the first year. The balance at the end of the first year is $412.

412 12 400 formula. balance the Use Pr Balance 12 formula ) 1 )( 03 . )( 400 ( interest simple the Use Pr         t P t I

SOLUTION

Step 2 Find the balance at the end of the second year. ANSWER Simon has $424.36 in his account after 2 years

36 . 424 36 . 12 412 formula. balance the Use Pr Balance 36 . 12 formula ) 1 )( 03 . )( 412 ( interest simple the Use Pr         t P t I

EXAMPLE 2

Computing Compound Interest using the Compound Interest Formula

Jackie deposits $325 in an account that pays 4.1% interest compounded

• annually. How much money will Jackie

have in her account after 3 years?

SOLUTION

Simplify 64 . 366 Add. ) 041 . 1 ( 325 for 3 & , for 0.041 P, for 325 Substitute ) 041 . 1 ( 325 formula interest compound the Use ) 1 (

3 3

      A A t r A r P A

t

ANSWER Jackie will have $366.64 in here account after 3 years