Dr Day Thur sday March 8 2012 Continuously Compounded Interest 53 Continuous Compounding compared to Periodic Compounding Solving Problems Whats the Unknown Thursday March 8 2012 ID: 527397
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Applied Calculus (MAT 121)Dr. Day Thursday March 8, 2012
Continuously Compounded Interest (5.3)Continuous Compounding compared to Periodic CompoundingSolving Problems: What’s the Unknown?
Thursday, March 8, 2012
MAT 121Slide2
Exponential FunctionsBig IdeasWhat are Exponential Growth and Exponential Decay?What sort of applications use exponential functions as their mathematical models?
What algebra do we need to remember to work with exponential functions?How do we undo exponentiation? We need the inverse function, called the logarithm function.Where does calculus fit in to all of this?Thursday, March 8, 2012
MAT 121Slide3
Using Logarithms to Solve EquationsHalley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above sea level is modeled by the function
p(x) = 29.92e-0.2x (x ≥ 0) If the barometric pressure as measured by a hot-air balloonist is 23.2 in. of mercury, what is the balloonist's altitude? Round your answer to two decimal places.
Thursday, March 8, 2012
MAT 121Slide4
Compound InterestPeriodic CompoundingA: amount in accountP: amount of original deposit (principal)i: annual interest rate, expresses as a decimal value
n: number of compounding periods per yeart: number of years the principal remains in accountContinuous CompoundingA: amount in accountP: amount of original deposit (principal)r
: annual interest rate, expresses as a decimal valuet: number of years the principal remains in
account
Thursday, March 8, 2012
MAT 121Slide5
Compound InterestSuppose $2500 is deposited in a savings account earning 1.25% annual interest compounded annually. Assuming no deposits or withdrawals, what will be the value of the account in 8 years?
What if the same the account used continuously compounded interest?Thursday, March 8, 2012MAT 121Slide6
Compound InterestAssume continuous compounding for the following problems.Calculate the amount accumulated after
3 years if $7800 is invested at 9% per year. How much of that is interest?Calculate the interest rate needed for an investment of $8,000 to grow to $10,000 in 10 years. Round to the nearest hundredth
of a percentage point.How long will it take for an investment of $7,000 to
double if the
investment earns interest at the rate of
3% per year?
Calculate the principal required in order to create an account with a value of $25000 after 3 years
at an interest rate of 12
% per year.
Thursday, March 8, 2012
MAT 121Slide7
WebAssign5.3 due tomorrow5.4 due Monday 3/19
Reminder: Check results for Test #3 Look at the multiple-choice correction sheet. Review the written comments I added to your test. Study the solution guide available on course website.
Assignments
Thursday, March 8, 2012
MAT 121