Percent - XYZ Custom Plus

346Chapter 5 PercentWe could have used this formula to find the interest in Examples 1 and 2. Inthose two cases, T is 1. When the length of time is in days rather than years,it is common practice to use 360 days for 1 year, and we write T as a fraction.Examples 3 and 4 illustrate this procedure.3. Another student takes out aloan like the one in Example 3.This loan is for $700 at 4%. Howmuch interest does this studentpay if the loan is paid back in 90days?Example 3A student takes out an emergency loan for tuition, books,and supplies. The loan is for $600 at an interest rate of 4%. How much interestdoes the student pay if the loan is paid back in 60 days?Solution The principal P is $600, the rate R is 4% = 0.04, and the time T is ​_60360 ​.Notice that T must be given in years, and 60 days = ​_60 ​year. Applying the formula,we have360I = P ⋅ R ⋅ TI = 600 × 0.04 × ​ 60 _360 ​I = 600 × 0.04 × ​_1 6 ​ ​60 _​ = 360 ​1 _I = 4The interest is $4.6 ​Multiplication4. Suppose $1,200 is deposited inan account that pays 9.5%interest per year. If all themoney is withdrawn after 120days, how much money iswithdrawn?Example 4A woman deposits $900 in an account that pays 6% annually.If she withdraws all the money in the account after 90 days, how much doesshe withdraw?Solution We have P = $900, R = 0.06, and T = 90 days = ​_90 ​year. Using360these numbers in the formula, we haveI = P ⋅ R ⋅ TI = 900 × 0.06 × ​ 90 _360 ​I = 900 × 0.06 × ​_1 4 ​ ​90 _360 ​= ​1 _4 ​I = 13.5MultiplicationThe interest earned in 90 days is $13.50. If the woman withdraws all the money inher account, she will withdraw$900.00 Original amount (principal)+ 13.50 Interest for 90 days$913.50 Total amount withdrawnThe woman will withdraw $913.50.BCompound InterestA second common kind of interest is compound interest. Compound interestincludes interest paid on interest. We can use what we know about simple interestto help us solve problems involving compound interest.5. If $5,000 is put into an accountthat pays 6% compoundedannually, how much money isin the account at the end of 2years?Answers3. $7 4. $1,238Example 5A homemaker puts $3,000 into a savings account that pays7% compounded annually. How much money is in the account at the end of 2years?Solution Because the account pays 7% annually, the simple interest at the endof 1 year is 7% of $3,000: