Get started today!

Good to have you back!
If you've signed in to StudyBlue with Facebook in the past, please do that again.

clifford y.

Math 618 Solution to Problem 2.2.15 r(12) = 12% = .12 implies monthly rate is 12%12 = 1% = .01. The quarterly rate is j = (1.01)3−1 = 0.030301, and the annual rate is i = (1.01)12−1 = 0.1268250301. For each year, the three payments on 4/1, 7/1, and 10/1 of $500 each are equivalent to an annual payment at the end of the year with the amount 500(1.030301)3 + 500(1.030301)2 + 500(1.030301) = 1592.753212. (This annual amount can also be obtained by the accumulated amount of four quarterly payments of $500 each subtract the last: 500s4|.030301 −500 = 1592.7532.) Using a calculator with equivalent annual payment of $1592.75 and annual rate of i = 0.1268250301, we can find the number of years needed to payoff the loan ($10,000): PMT =−1592.75, FV = 0, PV = 10000, T/Y = 12.6825% =⇒ N = 13.3239. So it takes a little over 13 years to payoff the loan. Using a calculator, we can find the present value of 13 annual payments: PMT =−1592.75, FV = 0, N = 13, T/Y = 12.6825% =⇒ PV = 9899.0912. So the 13 annual payments paid $9899.09 of the total $10,000. There is 10000−9899.09 = 100.91 to be paid by the last fractional payment. The last payment date is 13 years and 1 quarter from January 1, 2005 (or 53 quarters from January 1, 2005); it is April 1, 2018. The last payment is 100.91(1.030301)53 = 490.94. Answer: The last payment is $490.94 on 4/1/2018 Another Solution to Problem 2.2.15 r(12) = 12% = .12 implies monthly rate is 12%12 = 1% = .01. The quarterly rate is j = (1.01)3−1 = 0.030301, and the annual rate is i = (1.01)12−1 = 0.1268250301. For each year, the three payments on 4/1, 7/1, and 10/1 of $500 each are equivalent to an annual payment at the beginning of the year with the amount 500a3|.030301 = 1413.4876. Using a calculator with equivalent annual payment of $1413.49 at the beginning of the year and annual rate of i = 0.1268250301, we can find the number of years needed to payoff the loan ($10,000): (This is an annuity-due; set to BGN!) PMT =−1413.49, FV = 0, PV = 10000, T/Y = 12.6825% =⇒ N = 13.3238. So it takes a little over 13 years to payoff the loan. Using a calculator, we can find the present value of 13 annual payments: PMT =−1413.49, FV = 0, N = 13, T/Y = 12.6825% =⇒ PV = 9899.1277. So the 13 annual payments paid $9899.13 of the total $10,000. There is 10000−9899.13 = 100.87 to be paid by the last fractional payment. The last payment date is 13 years and 1 quarter from January 1, 2005 (or 53 quarters from January 1, 2005); it is April 1, 2018. The last payment is 100.87(1.030301)53 = 490.75. Answer: The last payment is $490.75 on 4/1/2018

Advertisement

Advertisement

"StudyBlue is great for studying. I love the study guides, flashcards and quizzes. So extremely helpful for all of my classes!"

Alice , Arizona State University"I'm a student using StudyBlue, and I can 100% say that it helps me so much. Study materials for almost every subject in school are available in StudyBlue. It is so helpful for my education!"

Tim , University of Florida"StudyBlue provides way more features than other studying apps, and thus allows me to learn very quickly!Â I actually feel much more comfortable taking my exams after I study with this app. It's amazing!"

Jennifer , Rutgers University"I love flashcards but carrying around physical flashcards is cumbersome and simply outdated. StudyBlue is exactly what I was looking for!"

Justin , LSU