Annuities If $1000 is invested at the end of each yearin an annuity that pays 8%, compounded annually,the number of years it takes for the future value toamount to $30,000 is given by t = log1.08 3.4. Usethe change of base formula to find the number ofyears until the future value is $30,000.

Annuities If $1000 is invested at the end of each yearin an annuity that pays 8%, compounded annually,the number of years it takes for the future value toamount to $30,000 is given by t = log1.08 3.4. Usethe change of base formula to find the number ofyears until the future value is $30,000.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 9E

See similar textbooks

Related questions

Q: A woman invests $5800 in an account that pays 6% interest per year, compounded continuously. (a)…

A: Given principal (P)=$5800 interest rate=6%=0.06 to find the amount at time in (a) and (b)

Q: Using either logarithms or a graphing calculator, find the time required for the initial amount to…

A: The formula for compound interest is A=P1+rnnt where A is the amount, P is the principle, r is the…

Q: 5. Jamie puts aside $10,000 in an account with interest compounded continuously at 2.7%. How long…

A: Amount invested=$10,000 Interest at 2.7% compound continuously To find time in months to earn $2,000…

Q: Moneysaver's Bank offers a savings account that earns 6% interest compounded continuously. If Aldo…

A: Given: The interest rate is 6% compounded continuously. Aldo deposits $2700. Since, the amount after…

Q: A favorite aunt wishes to establish a trust fund for her niece's math education. How much should she…

Q: A bank features a savings account that has an annual 5.2% with interest compounded percentage rate…

Q: esent value. A promissory note will pay $30,000 at maturity 10 years from now. How much should you…

Q: Investments How long, to the nearest year, will it take me to become a millionaire if I invest…

A: Let us assume P=principle= $1000 r= interest rate= 10%= 0.10 t=time in years=? A=annuity = $1000000

Q: In 1859, a person sold a house to a lady for $26. If the lady had put the $26 into a bank açcount…

A: Given that: In 1859, a person sold a house to a lady for $26. The lady had put the $26 into bank…

Q: An investment of $4,200 earns 7.8% annual interest, compounded continuously. If no funds are added…

A: The solution for the above question is as shown below.

Q: A bank features a savings account that has an annual percentage rate of r = 5.4% with interest…

A: It is given that Shantel deposits$4,000 in the account at annual rate of r=5.4%. The account balance…

Q: Use the model A=Pe" or A = P 1+ , where A is the future value of P dollars invested at interest…

A: We will find the time period of investment.

Q: Annuities If $2000 is invested at the end of each yearin an annuity that pays 5%, compounded…

A: A logarithm is the power to which a number must be raised in order to get some other number. Example…

Q: If $32,000 is invested in an account earning 6% interest compounded continuously, determine how long…

A: $32000 is invested in an account earning 6% interest compounded continuously. We have to find, how…

Q: A bank features a savings account that has an annual percentage rate of T = 4% with interest…

A: A bank features a savings account that has an annual percentage rate of r=4%with interest…

Q: A bank features a savings account that has an annual percentage rate of r = compounded quarterly.…

Q: Find the doubling time of an investment earning 6% interest if interest is compounded continuously.…

A: Given query is to find the time to double the investment, if compounded continuously.

Q: Use the model A=Pe^rt or A= P(1+r/n)^nt, where A is the future value of P dollars invested at…

Q: Finf the number of years required for a $2000 investment to triple at a 9% interest rate compounded…

A: Consider the following information: PrincipleP0=$2,000Rate of interestr=9⁒Principle after t…

Q: A bank features a savings account that has an annual percentage rate ofr = 5.4% with interest…

Q: A bank features a savings account that has an annual percentage rate of r = 2.9% with interest…

Q: Using either logarithms or a graphing calculator, find the time required for the initial amount to…

Q: C.A $9,000 inheritance is invested in a bond fund that earns 6% compounded continuously. How long…

A: For continuous compounding, A=Pert Here, P = $9,000, r = 6% = 0.06 and A = 3P = $27,000

Q: A family has saved $12,000 to purchase a new car. They would like to buy a car that costs $15,500…

A: by compound interest formula

Q: A bank features a savings account that has an annual percentage rate of r = 3.4% with interest…

A: Read the definition of each variable and you will get the answers in the question itself. Substitute…

Q: A bank features a savings account that has an annual percentage rate of r = 4% with interest…

Q: A family has saved $12,000 to purchase a new car. They would like to buy a car that costs $15,500…

A: It is compound interest problem.

Q: Assume there are no deposits or withdrawals An account now contains $3,640 and has been…

Q: Initially a patient is prescribed 20 milligrams of a certain medication by a physician to treat high…

Q: If you invest $200 into a savings account that earms 4% annual interest compounded continuously, how…

Q: A bank features a savings account that has an annual percentage rate of r = 5% with interest…

A: (A) It is given that r=5%. That is, r=5100=0.05 Also, Laura deposits $10,500 and is modeled by…

Q: 15. Student loan interest rates are currently 5.5% annually. Approximately how long will it take a…

A: We have to find the time in the given question.

Q: Use the model A = Pe^(rt) or A =P(1+(r)/(n))^(nt) where A is the future value of P dollars invested…

Q: Thanos just opened a savings account with an initial deposit of $20,000. The account pays 5% annual…

A: This question is based on compounding continuosly formula

Q: Question Jim invested $750 in a 3-year CD that earns 4.2% annual interest that is compounded…

A: Formula:A=PertA= amount of time tr=rate of interestP= initial amountGiven: P=$750 ,…

Q: Use the model A = Pet or A = P1+ for / years. nt , where A is the future value of P dollars invested…

Q: A bank features a savings account that has an annual percentage rate of r=5.9% with interest…

Q: Using either logarithms or a graphing calculator, find the time required for the initial amount to…

A: The equation of compound interest is given by; A=P1+rnnt Where; A→Final amountP→Principal…

Q: HIV/AIDS. In 2003 there were an estimated 25 million people who have been infected with HIV in…

Q: An investment of $1,000.00 earns 1.2% annual interest, compounded continuously. If no funds are…

Q: If $3500 is invested at an interest rate of 8.25% per year, compounded continuously, find the value…

Q: Starting at age 30, you deposit $2000 a year into an IRA account for retirement Treat the yearly…

A: To find the final amount of interest

Q: Moneysaver's Bank offers a savings account that earns 6.5% interest compounded continuously. If Deon…

Q: An account has $26,000 after 15 years. The account received 2.3% interest compounded continuously.…

Q: A bank features a savings account that has an annual percentage rate of r = 4.1% with interest…

Q: A bank features a savings account that has an annual percentage rate of r = compounded weekly. Julio…

A: Here a compound interest problem is given. For finding the solution for this problem we use the…

Q: A bank features a savings account that has an annual percentage rate of r = 2.1% with interest…

A: S=P1+rnnt P=3000 r=2.1% r=0.021 here compound interval is quarterly so take n=4

Q: A bank features a savings account that has an annual percentage rate of r = 4.6% with interest…

Q: A bank features a savings account that has an annual percentage rate of T = 5.7% with interest…

A: While calculating the total amount that will be left in the account which is compounded daily, the…

Q: Suppose you deposit $100 in the savings account where the interest earned is compounded continuously…

A: solution: Consider the given that: Primary money = P = $100 Let after n year the total balance…

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Annuities If $1000 is invested at the end of each year
in an annuity that pays 8%, compounded annually,
the number of years it takes for the future value to
amount to $30,000 is given by t = log_1.08 3.4. Use
the change of base formula to find the number of
years until the future value is $30,000.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: GIVEN AND OBJECTIVE

VIEW

Step 2: CALCULATION

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Recall the compound interest formula A=a(1+rk)kt. Use the definition of a logarithm along withproperties of logarithms to solve the formula for time t.
Trust Fund On the day of a child’s birth, a parent deposits $30,000 in a trust fund that pays 5 interest, compounded continuously. Determine the balance in this account on the child’s 25th birthday.
Recall the formula for continually compoundinginterest, y=Aekt. Use the definition of a logarithmalong with Properties of logarithms to solve theformula for time t such that tis equal to a singlelogarithm.
Suppose that $12,000 is invested in a saving account paying 5.6% interest per year. (a)Write the formula for the amount in the account after t years if interest is compounded monthly. (b)Find the amount in the after 3 years if interest is compounded daily. (c)How long will it take for the amount in the account to grow to $20,000 if interest iscompounded continuously?
Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.