# Refinancing a loan with penalty

Jeremy purchases a piece of construction equipment worth $26000 by paying 12% down and the balance with quarterly payments over 15 years at quarterly rate of 11% (i = 0.11/4). If he wants to refinance the loan, there is a penalty equal to one quarterly payment. If after 2 years he realizes he can borrow money from the bank at quarterly rate of 5% (i =0.05/4) . How much money does he save by refinancing? I start off by finding the loan is$22880 (88% of 26000). Find the quarterly payment of the first rate

22880 = PMT(1-(1+.11/4)^-60/(.11/4)

PMT = 782.96 (rounded up)

Refinance by finding accum amount after 2 years and adding on the penalty:

22880(1+.11/4)^8 - 782.96(1+.11/4)^8-1/(.11/4) = 21524.78423.

Find the new quarterly payment using the new rate:

21524.78423 = PMT (1-(1+.05/4)^-52/(0.05/4)) = $565.4338 (565.44 rounded up) Therefore he would've paid 782.96*60 = 46977.60, but he refinanced and paid 782.96*8 + 565.44*52 = 35666.56 Difference: 46977.6-35666.56 = 11311.04. Can someone help with this question thanks • Do you have another account called adam vincent? Also it would be helpful if you converted your post into latex – mrnovice Feb 25 '17 at 1:32 • That is my brother he is on the same ip address. – Alex Vincent Feb 25 '17 at 1:33 ## 1 Answer Here is how I would do it. 2 years in. Loan balance$\$21,525$ Quarterly payment $\$7835\%$is the prevailing interest rate. The present value of the next 52 quarters of$\$783$ payments evaluated at the market rate is. $\$ 29,805$Or pay$\$783$ penalty. Add that to the current loan balance, and you get $\$22,308$• What do you mean I dropped a 0 early in my calculations, the loan was only 26,000 not 260,000 – Alex Vincent Feb 25 '17 at 2:12 • Ha, so I added a 0! okay, I will fix my numbers. – Doug M Feb 25 '17 at 2:13 • So how much would he save overall by refinancing, also you rounded to the nearest dollar and not rounded up to the nearest penny so the number would be slightly off. I think I get the idea but want to verify the correct answer – Alex Vincent Feb 25 '17 at 2:16 • I have$\$7,497.49$ – Doug M Feb 25 '17 at 2:17
• Hmm apparantely the answer is still wrong – Alex Vincent Feb 25 '17 at 2:21