Suppose a business makes a profit an rate of $100,000 per year (this rate is cal

Question

Suppose a business makes a profit an rate of $100,000 per year (this rate is called an income stream) over a 5 year span. This profit is reinvested at a rate of 6% per year, compounded continuously. Find the future value at the end of 5 years as follows: Assume the business makes a deposit of $100,000 at the start of each year. Find the future value of each of these deposits at the end of 5 years. Fill out the table below. Round answer to the nearest whole number. Include correct units. Based on our assumptions in part (a), how much is this income stream worth at the end of 5 years suppose this business makes more regular deposits such as monthly, weekly, daily, or continuously, would this effect the future value of the income stream For example if the deposits were daily (about $280.90 a day), would the future value of this income stream be greater than, less than, or the same as if it were deposited once a year Greater than The same as Less than Suppose the deposits were made continuously, write an integral formula for the future value of this income stream. Evaluate this integral to find the future value of this income stream. Round answer to nearest whole number. Include units.

Explanation / Answer

Compounded Future Value = Present Value * e rt

Here, Present Value = $ 100,000

r = Compounded rate of interest = 6%

t = no. of years for which the amount invested.

Recall that e stands for the Napier's number (base of the natural logarithm) which is approximately 2.7183.

So, Solution to this problem is :

* e = 2.7183

Year the deposit was made t = no. of years for which the amount invested. Value of the deposit at the end of 5th year ($) 1 5 100,000 * e(0.06 * 5) = $134,986 2 4 100,000 * e(0.06 * 4) = $127,125 3 3 100,000 * e(0.06 * 3) = $119,722 4 2 100,000 * e(0.06 * 2) = $112,750 5 1 100,000 * e(0.06 * 1) = $106,184 Worth of the income stream at the end of 5 years = Sum of the Values of the deposits at the end of 5th year = $ 600,767

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