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U of U MATH 1030 - Quiz 4

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Quiz 4: Sec 4B - 4CSpring 2008 MATH 1030-0081. (6 Points) C alculate the APY (to three decimal places) for an account that has an APR of8.3% assuming thata) interest is compounded monthly.b) interest is compounded daily.a) We first want to find the accumulated balance after 1 year. Note that n = 12 for monthlycompounding. We haveA = P ×1 +0.0831212= 1.086231401P.Now, we want to find the relative change in the balance over the course of this one year.Relative change =1.086231401P − PP= 0.086231401The APY is this relative change as a percentage. Th erefore, APY = 8.623%.b) Using the same precedure as above, we see thatA = P ×1 +0.083365365= 1.086531556PandRelative change =1.086531556P − PP= 0.086531556.Therefore, the APY is 8.653%.2. (7 Points) You deposit $1000 into an account with an APR of 3.62%. How much will you haveafter 15 years assuming that you havea) simple interest.b) interest compounded quarterly.c) interest continuously compounded.a) First, note that the interest from year to year does not change when calculating simple interest.Interest per year = 0.0362 × 1000 = 36.20Total Interest = 15 × 36.20 = 543A = 1000 + 543 = 1543b) We want to use the compounded n times a year interest formula with APR = 3.62%, n = 4,P = 1000, and Y = 15.A = 1000 ×1 +0.036244×15= $1716.971c) Here, we want to use the continuous compounding formula with APR = 3.62%, P = 1000, andY = 15.A = 1000 × e0.0362×15= $1721.173. (7 Points) You decide that you want to build a college fund for your children that has an APRof 5.25%. To do this, you will deposit $50 every week for 20 years.a) How much will you have in the college fu nd after 20 years?b) How much did you d eposit into the college fund over the 20 year period?c) How much of the college fund is from the interest alone?a) We want use the savings plan formula with APR = 5.25%, n = 52, PMT = 50, and Y = 20.A = 50 ×1 +0.05255252×20− 10.052552= $91, 923.02b) We then have thatTotal Deposited = 50 × 52 × 20 = $52, 000.c) Therefore,Interest = $91, 923.02 − $52, 000 = $39,


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U of U MATH 1030 - Quiz 4

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