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- HOW MUCH WOULD YOU NEED TO DEPOSIT IN AN ACCOUNT NOW IN ORDER TO HAVE $3,000 IN THE ACCOUNT IN FIVE YEARS? ASSUME THE ACCOUNT EARNS 3% INTEREST COMPOUNDED MONTHLY. WELL BE USING THE COMPOUNDED INTEREST FORMULA TO SOLVE THIS PROBLEM. IF WE TAKE A LOOK AT THESE TWO FORMULAS HERE BELOW, THEY ARE EQUIVALENT BUT USE DIFFERENT VARIABLES TO REPRESENT THE SAME QUANTITIES. THIS FIRST FORMULA IS PROBABLY A MORE COMMON COMPOUNDED INTEREST FORMULA, BUT OUR TEXT BOOK DOES USE THIS FORM OF THE EQUATION HERE. WHERE THE ACCOUNT BALANCE AFTER A CERTAIN AMOUNT OF TIME IN THIS FORMULA IS A, IN THIS FORMULA ITS P SUB N, P IN THIS FORMULA AND P SUB ZERO IN THIS FORMULA REPRESENT THE STARTING AMOUNT OR THE PRESENT VALUE OR AS THE ANNUAL INTEREST RATE EXPRESSES A DECIMAL IN BOTH FORMULAS. IN THIS FIRST FORMULA, N IS THE NUMBER OF COMPOUNDS PER YEAR. NOTICE HOW N OCCURS HERE AND HERE. IN OUR SECOND FORMULA, K IS THE NUMBER OF COMPOUNDS PER YEAR WHICH OCCURS HERE AND HERE. AND THEN FINA
