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

D AY 86 – I NTRODUCE THE POWER OF INTEREST

V OCABULARY 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.

E XAMPLE 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?

S OLUTION In the simple interest formula, time is measured in years. Write 1 8 18 months as , or 1.5 years. Write the annual interest rate 1 2 as a decimal.  Pr Use the formula for simple interest I t  ( 725 )( 0 . 023 )( 1 . 5 ) Substitute $725 for ,0.023 for , & 1.5 for I P r t  $ 25 . 01 Multiply I ANSWER Diana will earn $25.01 in interest

E XAMPLE 2 FINDING THE BALANCE You deposit $300 in a savings account that pays 4% simple annual interest. Find your account balance after 9 months.

S OLUTION 9 Write 9 months year , or 0.75 year. 1 2   Pr Write the balance formula A P t   300 ( 300 )( 0 . 04 )( 0 . 75 ) Substitute $300 for P, 0.04 for , & 0.75 for . r t   300 9 Multiply.  309 Add. ANSWER Your account balance after 9 months is $309

V OCABULARY 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

E XAMPLE 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?

S OLUTION Step 1 Find the balance at the end of the first year.  Pr Use the simple interest I t  ( 400 )( 0 . 03 )( 1 ) formula  12   Balance Pr Use the balance formula. P t   400 12  412 The balance at the end of the first year is $412.

S OLUTION Step 2 Find the balance at the end of the second year.  Pr Use the simple interest I t  ( 412 )( 0 . 03 )( 1 ) formula  12 . 36   Balance Pr Use the balance formula. P t   412 12 . 36  424 . 36 ANSWER Simon has $424.36 in his account after 2 years

E XAMPLE 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?

S OLUTION   t ( 1 ) Use the compound interest formula A P r   3 325 ( 1 0 . 041 ) Substitute 325 for P, 0.041 for , & 3 for A r t  3 325 ( 1 . 041 ) Add. A  366 . 64 Simplify A ANSWER Jackie will have $366.64 in here account after 3 years