Question 1Morey flows into the coffers of Grinch Enterprises at the ratef(t) = 400t + 2000for T = 20 years.(a) The total money flow for Grinch Enterprises is[Select](b) Assuming that the interest rate during this period is r = 4%, thepresent value of this money flow is [Select]

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Answered: Money flows into the coffers of Grinch…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years Step 1 Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage. The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known. To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an interest rate of i per period, use the formula PMT = PV The given mortgage is $100,000, so PV = 100000 The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = 12 Step 2 With PV = 100,000, i = If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300 nearest cent. PMT = PV PMT = = 1 − (1 + i)¯″¸ 100000 0.043 and n = "I 12 544.54…
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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 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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Money flows into the coffers of Grinch Enterprises at the rate f(t) = 400t + 2000 for T = 20 years. (a) The total money flow for Grinch Enterprises is [Select] (b) Assuming that the interest rate during this period is r = 4%, the present value of this money flow is [Select]