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#1
05-30-2015, 01:58 AM
 mc2147 SOA Join Date: May 2015 Posts: 1
ASM Practice Exam Question 6

Jan gives Ted a loan at 4% effective to be repaid by 10 annual payments of 100, followed by 5 annual payments of 200. Just after Ted makes the 5th payment, Jan and Ted discover that the payments should have been 10% higher than they were originally scheduled. They agree that Ted will make increased payments of K in the 6th through 10th years to adjust for error. The payments of 200 in the 11th to 15th years will not change . Determine K.

This is how I approached it:
I find the AV of both scenarios at the end of 15 years and set them equal

110 s angle 10 + 220 s angle * I^10 = 100 s angle 5 + K * s angle 5 * I^5 + 200 s angle 5 * I^10

However, the solution gives a different number. The book solves this by equating the outstanding balances at t = 5. How is this different from the AV method?

Last edited by mc2147; 05-30-2015 at 02:17 AM..
#2
05-30-2015, 10:14 AM
 Steve Paris Note Contributor SOA Join Date: Aug 2005 Location: FSU (Go NOLES!!) Favorite beer: Cold Posts: 135

Quote:
 Originally Posted by mc2147 Jan gives Ted a loan at 4% effective to be repaid by 10 annual payments of 100, followed by 5 annual payments of 200. Just after Ted makes the 5th payment, Jan and Ted discover that the payments should have been 10% higher than they were originally scheduled. They agree that Ted will make increased payments of K in the 6th through 10th years to adjust for error. The payments of 200 in the 11th to 15th years will not change . Determine K. This is how I approached it: I find the AV of both scenarios at the end of 15 years and set them equal 110 s angle 10 + 220 s angle * I^10 = 100 s angle 5 + K * s angle 5 * I^5 + 200 s angle 5 * I^10 However, the solution gives a different number. The book solves this by equating the outstanding balances at t = 5. How is this different from the AV method?
There's nothing wrong with your approach. It's your equation that's messed up. For example, the first term on the LHS of your equation should be 110 s angle 10 * (1.04^5).
__________________
Steve Paris, Ph.D, ASA
paris@math.fsu.edu

 Tags annuity, exam, exam fm, loan