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Compound Interest (Finite Number of Calculations)  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
One real world application of exponential equations is in compound interest. The formula for compound interest with a finite number of calculations is an exponential equation. We can solve for a parameter of this equation, and can use logarithms to access parameters in the exponent. Students may be asked to solve compound interest problems with interest compounded biannually, monthly, or daily.
Compounding interest, so what compounding interest is basically you have an investment you put a certain amount of money into an account and interest is calculated a set number of times per year okay? So what we're dealing now is this formula right here is for a set number of times that interest is calculated. It could be daily, monthly, weekly, annually once a year all different sorts of different ways that interest can be calculated and the formula reflects all those different things okay? So what we have is a is equal to p 1+r over n to the nt. Okay and what I have written down here is what each of those variables stands for.
Okay a is just going to be your ending amount okay? p is stands for principal another way of saying starting amount so if you invest $2,000, p would be 2,000 okay? Rate is going to be your percent interest so say you get 4% you'll always need to put in as a decimal so that 4% becomes 0.04 okay, n is the number of times per year interest is calculated okay so if it's daily you put in 365, weekly 52 weeks an year put in 52, monthly 12 quarterly means 4 times a year so 4 so on and so forth okay so n is just the number of times an interest is calculated and lastly t is the time of investment in years.
Okay so sort of we're looking formula lot of variables going on but overall just 5 things we have to consider interest, amount you put in the amount that comes out rate [IB] number of times this is calculated and the length of time of your investment.
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Carl Horowitz
B.S. in Mathematics University of Michigan
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Sample Problems (7)
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Compound Interest (Finite Number of Calculations)
Problem 1 6,824 viewsYou invested $3000 in an account that earns 4% interest.
How much will you have after 4 years if interest is compoundeda) biannuallyb) monthlyc) daily 
Compound Interest (Finite Number of Calculations)
Problem 2 5,820 viewsInvest $5000 at 5% interest compounded quarterly.
How long to double the investment? 
Compound Interest (Finite Number of Calculations)
Problem 3 1,365 views 
Compound Interest (Finite Number of Calculations)
Problem 4 1,479 views 
Compound Interest (Finite Number of Calculations)
Problem 5 1,441 views 
Compound Interest (Finite Number of Calculations)
Problem 6 1,335 views 
Compound Interest (Finite Number of Calculations)
Problem 7 1,448 views
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angel · 7 months, 3 weeks ago
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