math quiz
compound interest formula
A = P(1 + r/n)^(n x t), r is the rate, n is the number of times compounded, t is time
formula for continuous compounding
A = P*e^rt
Explain why the term APR/n appears in the compound interest formula for interest paid n times a year.
APR represents the annual percentage rate (as a decimal). To account for the interest paid n times a year, this annual (yearly) rate needs to be divided by the number of compounding periods per year, n.
What is continuous compounding? How does the APY for continuous compounding compare to the APY for, say, daily compounding? Explain the formula for continuous compounding.
Compounding infinitely many times per year is called continuous compounding. The APY for continuous compounding is only slightly larger than the APY for daily compounding. The formula for continuous compounding is a special form of the compound interest formula.
Given a half-life, explain how you calculate the value of an exponentially decaying quantity at any time t.
Let t be the amount of time that has passed and Upper T Subscript ha l fThalf be the half-life. The quantity after time t is the original quantity times this factor of left parenthesis one half right parenthesis Superscript t divided by Upper T Super Subscript ha l f 1 2t/Thalf
Describe the basic differences between linear growth and exponential growth.
Linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time.
What is the difference between simple interest and compound interest? Why do you end up with more money with compound interest?
Simple interest is interest paid only on the original investment whereas compound interest is interest paid both on the original investment and on all interest that has been added to the original investment. Since compound interest is calculated based on a larger amount than simple interest, it results in a larger amount of money over time.
Human population has been growing exponentially for a few centuries, and this trend can be expected to continue forever in the future.
The statement does not make sense because exponential growth cannot continue indefinitely.
A small town that grows exponentially can become a large city in just a few decades.
The statement makes sense because exponential growth leads to repeated doublings, making the population increase rapidly.
Money in a bank account earning compound interest at an annual percentage rate of 3% is an example of exponential growth.
The statement makes sense because the money in the account grows by the same percentage, which is an example of exponential growth
APY
absolute increase/ starting principle
log 10 pi
log=between 0-1 pi= 1-10
Briefly describe exact doubling time and half-life formulas. Explain all their terms.
no negative; fractional growth decay no log102; fractional decay
