Checklist. Assignment

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1 Checklist Part I Fid the simple iterest o a pricipal. Fid a compouded iterest o a pricipal. Part II Use the compoud iterest formula. Compare iterest growth rates. Cotiuous compoudig. (Math 1030) M B 1 / 15 Assigmet Assigmet: 1. p 223 Quick Quiz 2. (Part I) p 224 Excercises 43, 45, (Part II) p 225 Exercises 49, 51, 53, 55, 59, 60, 65, 68, 71, For a algebra review, p 224 Exercises Practice usig your calculator! (Math 1030) M B 2 / 15 Key Words - Part II for Iterest Paid Oce a Year for Iterest Paid More tha Oce a Year for Cotiuously Compouded Iterest Aual Percetage Rate The iterest rate whe iterest is compouded just oce a year. Aual Percetage Yield The relative icrease of a balace over oe year. (Math 1030) M B 3 / 15

2 Compoudig Iterest Oce A Year The balace at the ed of year 1 was the startig pricipal times 1.05: $ = $1050. The balace at the ed of year 2 was the year 1 edig balace times 1.05: $ = $1000 (1.05) 2 = $ Ad the third year edig balace is the year 2 edig balace times 1.05: $ = $1000 (1.05) 3 = $ (Math 1030) M B 4 / 15 Compoudig Iterest Oce A Year Cotiuig this patter, we ca geeralize the edig balace after N years is the startig pricipal times 1.05 raised to the Nth power. For istace, after N = 20 years, the balace is $1000 (1.05) 20 = $ Example Use your calculator to fid the accumulated balace after 15 years. (Math 1030) M B 5 / 15 (For Iterest Paid Oce A Year) A = P (1 + APR) Y (1) A is the accumalated balace after Y years P is the startig pricipal APR is the aual percetage rate (as a decimal) Y is the umber of years (Math 1030) M B 6 / 15

3 Suppose you ivest $100 i two accouts. Both pay 10% per year, but oe pays simple iterest ad oe pays compoud iterest. Make a table that shows the growth of each accout over a 5-year period. Use the compoud iterest formula for the results for the secod accout. Make a chart showig the growth of each accout. (Math 1030) M B 7 / 15 Suppose you deposit $100 ito a bak that pays compoud iterest at a APR of 10%. Now assume it pays the iterest quarterly. The the quarterly iterest rate is APR / 4, or 10%/4 = 2.5%. The table below shows the accout growth each quarter. N quarters Iterest Paid New Balace 1st Q 2.5% $ = $2.50 $ d Q 2.5% $ = $2.56 $ rd Q 2.5% $ = $2.63 $ th Q 2.5% $ = $2.69 $ (Math 1030) M B 8 / 15 (For Iterest Paid More Tha Oce A Year) ( A = P 1 + APR ) (Y ) (2) A is the accumalated balace after Y years P is the startig pricipal APR is the aual percetage rate (as a decimal) is the umber of compoudig periods per year Y is the umber of years (Math 1030) M B 9 / 15

4 You ivest $3,000 for 15 years with a APR of 4.5% ad mothly. How much moey will accumulate? Compare this amout to the amout you would have if iterest were paid oly oce each year. Note the APR is the same i both cases. Oe accout pays more, though! (Math 1030) M B 10 / 15 The previous example compares compoudig oce a year with compoudig mothly. For the first year. the iterest eared is $135 ad $ respectively. The APR for both are the same (4.5%), but the effective yield of compoudig mothly is higher. This relative icrease is APY: $ = = 4.594% $3000 The over oe year, APY = absolute icrease startig pricipal. (Math 1030) M B 11 / 15 Example You deposit $1000 ito a accout with APR = 8%. Fid the aual percetage yield with mothly compoudig ad daily compoudig. Method: Fid the accumulated balace at the ed of oe year. The take the absolute ad relative differeces with startig pricipal as the referece value. (Math 1030) M B 12 / 15

5 Cotiuous Compoudig What if the iterest were compouded more ofte? (Every hour or miute or secod!) The previous example gives APR = 8% (compouded aually), APY = 8.3% (compouded mothly), APY = 8.328% (compouded daily). The APY icreases, but the chage gets smaller as the iterest compouds more frequetly. If we ca compoud ifiitely may times per year, or cotiuously, this would ot grow above a certai amout. (Math 1030) M B 13 / 15 Cotiuous Compoudig APY APY % % % % % 10, % The Cotiuous Compoudig Formula A = P e APR Y (3) e is a special umber with a value e (Math 1030) M B 14 / 15 Usig backwards Compoudig Iterest Suppose you wat to create a college fud for a ewbor. How much should you ivest ow to have a future value of $100,000 i a accout promises APR = 3%, compouded mothly, i 18 years? ( A = P 1 + APR ) ( Y ) Divide both sides by ( ) 1 + APR ( Y ), iterchage the left ad right sides, A P = ( ) 1 + APR ( Y ) (Math 1030) M B 15 / 15

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