PDA

View Full Version : Need Help on a Sinking Fund Problem

loveitlive
April 11th 2006, 10:16 PM
Hi, I have trouble soloving this problem,

Joe repays a loan of 10,000 by establishing a sinking fund and making 20 equal payments at the end of each year. The sinking fund earns 7% effective annually. Immediately after the fifth payment, the yield on the sinking fund increases to 8% effective annually. At that time Joe adjusts his sinking fund payment to x so that the sinking fund will accumulate to 10,000 20 years after the original loan date. Determine x

Thank you

wat
April 11th 2006, 10:26 PM
Hi, I have trouble soloving this problem,

Joe repays a loan of 10,000 by establishing a sinking fund and making 20 equal payments at the end of each year. The sinking fund earns 7% effective annually. Immediately after the fifth payment, the yield on the sinking fund increases to 8% effective annually. At that time Joe adjusts his sinking fund payment to x so that the sinking fund will accumulate to 10,000 20 years after the original loan date. Determine x

Thank you

Work it in two parts.

Part 1: Find X1, which is the payment under the 7% planned yield. This should be (10,000) / s_20|.07 .

Part 2: Find X2, which is the amount you'll pay 15 times from time 6 to time 20. However, you already paid (X1)*s_5|.07.

So, the amount you have to amortize over 15 years is:

10,000 - (X1)*(s_5|.07)*(1.08^15)

since the first five payments into the fund will accumulate in the sinking fund at 8%, not 7%, after the first 5 years.

Thus, the X2 you should be looking for is:

[10,000 - (X1)*(s_5|.07)*(1.08^15)] / (s_15|.08)

I apologize for the bad notation - hopefully this can break it down for you.

loveitlive
April 11th 2006, 11:05 PM
Thank you so much for the help!