Quiz 3 - Financial MathMath 1030 - Dylan Zwick’s C lassFall 2007Name:Here are the formulas you may nee d :Compound Interest Formula for Annual CompoundingA = P × (1 + AP R)YCompound Interest Formula for Interest Pa id n Times Per YearA = P1 +AP RnnYCompound I nterest Formula for Continuous CompoundingA = P × eAP R×YSavings Plan Formula (Regular Payments)A = P MT ×1 +AP RnnY− 1AP RnVariable DefinitionsA = Accumulated AmountP = Starting PrincipalAPR = Annual Percentage R ate (express as a decimal)Y = Number of Yearsn = Number of Compounding Periods per YearPMT = Regular Payment11. Different Compounding Periods - 15 pointsSuppose you invest $2, 500 in an account that generates compoundintere st with an APR of 5% for 30 years.(a) If your account compounds every year, how much money willyou have in the account after 30 years? (3 points)(b) If your account compounds every month, how much moneywill you have in the account after 30 years? (3 points)(c) If your account compounds continuously, how much moneywill you have in the account after 30 years? (3 points)2(d) What is the APY (annual percentage yield) of the account if itcompounds continuously? (3 points)(e) Suppose that instead of generating compound interest the ac-count generated simple intere st with an APR of 5%. How muchmoney would you have in the account after 3 0 years? (3 points)32. Savings Plan - 10 points(a) Suppose you start a retirement savings plan when you’re 30 andwant to retire with $2, 000, 000 35 yea rs later. If you invest inan account with a 4.5% APR compounded monthly, and youmake monthly payments, how much money will you need toput away every month in order to retire with $2, 000, 000?(5 points)Note - The savings plan formula assumes compounding at thesame rate as you make payments. This is the case for this prob-lem.(b) What is the total amount of money that you invest in this ac-count over the 35 years? (2 points)4(c) Suppose that instead of putting away the money in monthly in-stallments you invest one lump sum at the start and let it accu-mulate interest for 35 years in this account. How much moneywould you need in this lump sum in order to have $2, 000, 000after 35 years? (3 points)53. Extra Credit - 5 points(a) Suppose you invest $5, 000 in a compound intere st savings ac-count with an APR of 5% that compounds annually. After Ynumber of years you ha ve $17, 778.36 in your account. What isY ? (Hint - logarithms) (4 points)(b) Name one character that appears in more than 3 of Shakespeare’splays. (1 point)More Extra Credit - Wednesday of next wee k is Halloween. We willhave a costume contest the first 5 minutes of class. The people withthe top 3 costumes, chosen democratically, will be a wa rded extracredit points on this quiz.Best Costume - 3 pointsRunner Up - 2 pointsSecond Runner Up - 1
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