30. Compound interest. The amount of money, A(t), in asavings account that pays 6% interest, compoundedquarterly for t years, when an initial investment of$2000 is made, is given byA(t) = 2000(1.015)“.a) Find A(3).b) Find A(5).c) Find A(5) – A(3).A(5) - A(3)d) FindWhat rate of change does this5 - 3represent?

Answered: 30. Compound interest. The amount of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ )". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.
A college student has invested $4200 in an account that pays 1.6% interest compounded monthly. Which of the following equations could be used to find the amount in the account after 11 years? 12.11 1.6 O 4200( 1+ 12 O (4200)(0.016)(11) 12-11 0.016 4200( 1+ 12 4200e1.6-11 O 4200e0.016 - 11
3. The initial amount for J.W.'s new bank account is $2,500. The total amount in the bank account, a(t), for J.W. after t years can be represented by a(t) = 2500(1+). If J.W. has $4,400 in the bank account at the end of 6 years without putting any more money in the account, what is the value of x?
The amount that should be set aside is $ (Round up to the nearest dollar.)
The formula for computing the amount of money in a savings account with an r% annual in- r t erest rate (compounded each year) t years after opening with $P is given by A(t) = P (1 + 100 o compound each year (or annually) means that the interest is computed and added to the ac- ount once a year. The interest the next year is computed on the new account value (with the revious year's interest included). 1. Eloisa plans to put $200 in a savings account with a 3.5% annual interest rate. (a) Write a function for how much money will be in the account in t years. (b) How much will be in the account after 5 years? (c) How long will it take to have $400 in the account? Explain how you found your answer.
Find the principal invested (P) of amount (A )invested at rate (r )for (t) years, compounded (n) times per year if A = $10,000, r=6.5%, t=6 , n=12 .
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The time, t, in years for an amount increasing at a rate of r (in decimal form) to In 2 This is called the doubling time. Find the doubling time to the nearest tenth for an investment at an interest rate of 7% = 0.07. double is given by t = In (1+r) The doubling time is years. (Round to the nearest tenth of a year.)
Match the formula with the appropriate amount of times compounded per year. A(t) = P(1+r)t Annually Monthly Weekly Quarterly Continuously 1. 2. 3. 4t A(t) = P(1 + ² ) ¹² 4 12t A(t) = P(1 + ₂ ) ¹²² 12 A(t) = P(1+2) 52t 52 5. A(t) = Pert
The value of the account will be $ enter your response here. (Round to the nearest dollar as needed.)
A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+)". This is n because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) = Pert , and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning. Why can we write nt lim,→00 P(1+ )"t P limn¬∞ (1+)™ ? n

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