math quiz

¡Supera tus tareas y exámenes ahora con Quizwiz!

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


Conjuntos de estudio relacionados

Public Speaking Final Study Guide

View Set

Chapter 1: Managerial Accounting

View Set