You run an online business and you are considering an upgrade to your website. The upgrade will cost you a one-time fee of $8,000 today. You expect that the upgrade will generate an additional profit flow of $5,000 per year. (This income stream is continuous and constant.) Assume that the interest rate is 8% compounded continuously. How long will it take for the upgrade to “pay for itself”? In other words, over what period of time will the present value of the additional profit generated by the upgrade be equal to the cost of the upgrade itself?

Q: Avery is going to invest $270 and leave it in an account for 20 years. Assuming the interest is…

A: For compounded continuously  A=Pertr = ln(AP)t   Here,  A=$600P=$270t=20

Q: To provide for a future expansion, a company plans to make continuous deposits to a savings account…

A: A differential equation is an equation that usually relates a function with with its derivatives.…

Q: A math tee shirt business is expected to generate $41,000 in revenue per year for the next 20 years.…

A: The options for expression are not given here. Given : There is a continuous stream of a payment…

Q: Find the years it will take for a principal P to double if invested at a rate of 4% compounded…

A:

Q: 1. How many whole years will it take money to be four times (itself) its value at the rate of 7%…

A: Topic - compound Interest Note: as per bartleby guidelines,we are supposed to solve only first…

Q: A new truck costing $50,000 with a residual value of $4,000 has an estimated useful life of five…

A: given that new truck cost = $50,000 residual value = $4,000

Q: If you borrow $8,500 at 4% interest, what is the amount that you will owe in five years if…

A: To find the amount owe in 5 years if compounding continuously :

Q: Find the accumulated present value of a 11-year $70,000 continuous income stream that has been…

A:

Q: Suppose that you have $10,000 to invest. Which investment yields the greatest return over 5 years 5%…

A:

Q: Jay wants to invest $5,000 in an account with an interest rate of 8.5% that is compounded MONTHLY.…

A:

Q: Assume that you can earn 6% on an investment, compounded daily. Which of the following options would…

A:

Q: One hundred shares of a technology stock were purchased on January 2, 1990, for $1200 and sold on…

A:

Q: This exercise is based on the following table, which lists interest rates on long-term investments…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Max was injured and can no longer work. As a result of a lawsuit, he is to be awarded the present…

A: Concept: We have the present value (PV) If the rate of receipt of revenue from time t=a to b is R(t)…

Q: Find the principal P that must be invested at rate r =6%, compounded monthly, so that $1,000,000…

A: Given information, Amount A=$1000000 interest rate r=6%=0.06 Time t=40 years number of times…

Q: A zero-coupon bond can be redeemed in 20 years for $10,000. How much should you be willing to pay…

A: Given: Total years=20……1Redeemed amount=$10,000……2

Q: An investment fund pays 5% per year, compounded semi-annually, on all money invested. How much must…

A:

Q: Find the present value of a continuous income stream of ​$18​,000 per year for 20 years at 2.8​%…

A:

Q: If $1000 isinvested for x years at 8% compoundedquarterly, the future value of the investment is…

A: Given data, The amount of $1000 is invested for x number of years at the rate of 8% compounded…

Q: Camden is going to invest $600 and leave it in an account for 12 years. Assuming the interest is…

A: Solve for the rate of interest

Q: Find the effective yield of an investment that earns 4.1% compounded quarterly.

A:

Q: If investment A has an annual return of 3% with continuously compounded interest, and Jane has $400…

A: Given data- Amount (A) = $400. Rate (R) = 3%. Time (n) = 5 years. We have to find the amount of jane…

Q: This exercise is based on the following table, which lists interest rates on long-term investments…

A:

Q: Find the accumulated present value of an investment over a 7 year period if there is a continuous…

A: Given, R(t) = 5000 T    = 10 years K    = 2%

Q: What interest rate, to the nearest tenth of a percent, is required for an investment subject to…

A: Let P be the principal amount.

Q: An investment fund pays 10% per year, compounded quarterly, on all money invested. How much must be…

A:

Q: This exercise is based on the following table, which lists interest rates on long-term investments…

A: The rate of interest in United States is 2.5%. r=0.025 The interest is compounded annually. m=1…

Q: If an IRA is a variable-rate investment for 25 years at rate r percent per year, compounded monthly,…

A:

Q: Suppose that you have children young, pay for their college expenses, and finally start saving for…

A:

Q: Ella is going to invest $18,000 and leave it in an account for 8 years. Assuming the interest is…

A:

Q: An investment fund pays 9% per year, compounded quarterly, on all money invested. How much must be…

A:

Q: If the present value of my investment is $1,000 and the rate of interest is 10% compounded annually,…

A: From the given information, present value of my investment is $1,000 that is P = 1000, the rate of…

Q: Suppose you invest $5000 and would like your investment to grow to $10,000 in eight years. What…

A: Given that the initial amount= P=5000 Final amount=A= 10000 Time=t= 8 years  n=number of times…

Q: Someone invests a constant stream of $450 per year at a continuously compounding interest rate of…

A: To calculate the present value of the investment following the (continuous) exponential model

Q: At what rate is the account growing?

A:

Q: Find the present value of a $45, 000 annual income stream if it is invested immediately as it is…

A:

Q: A new restaurant is expected to produce a continuous income stream at the rate of R(t) = 100,000…

A: Here the present income R(t)=100000 Interest rate (r)=4% Time(t)=5 year The income stream is…

Q: The Megabucks Corporation is considering buying OHaganBooks.com. It estimates OHaganBooks.com's…

A: To estimate O'HanganBooks.com revenue stream at $30 million per year, growing continuously at a 10%…

Q: Elon Musk asks you to invest $10M in his new cyber scooter product. He promises that he will return…

A: Find the interest rate that so that Jim's offer is better than that of Elon as follows.  Elon asks…

Q: Carter is going to invest $79,000 and leave it in an account for 12 years. Assuming the interest is…

A: Simply use the formula for compound interest.

Q: . An investment fund pays 12% per year, compounded monthly, on all money invested. How much must be…

A:

Q: Find the present value of a $8,000 annual income stream if it is invested immediately as it is…

A: Compound continuously A=Pe^(rt)

Q: Find the accumulated value of an investment of $25,000 for 4 years at an interest rate of 6% if the…

A:

Q: if changing market condition cause a company earning 8000000 in 2005 to project a loss of 2 percent…

A: Given that, the earning in 2005 is 80,00,000 and each of the next 5 year the loss is 2% of its…

Q: Perpetuity is derived from the fact that the number of compounding periods approaches to infinity…

A: Perpetuity is derived from the fact that the number of compounding periods approaches to infinity…

Q: Which of the following investment opportunities offers you the best effective rate of return?…

A: Let us take the time of 1 year and see the compounding value. The formula for compound interest is:…

Q: Morgan is going to invest $8,200 and leave it in an account for 10 years. Assuming the interest is…

A: A=$16500 P=$8200 t=10 years n=12 (compounded monthly) We have to found intrest rate

Q: This type of calculation assumes the payment is to be done once a year while the compounding occurs…

A: