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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

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  • $\begingroup$ Do you have another account called adam vincent? Also it would be helpful if you converted your post into latex $\endgroup$ – mrnovice Feb 25 '17 at 1:32
  • $\begingroup$ That is my brother he is on the same ip address. $\endgroup$ – Alex Vincent Feb 25 '17 at 1:33
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Here is how I would do it.

2 years in.

Loan balance $\$21,525$ Quarterly payment $\$783$

$5\%$ 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 $\$22,308$

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  • $\begingroup$ What do you mean I dropped a 0 early in my calculations, the loan was only 26,000 not 260,000 $\endgroup$ – Alex Vincent Feb 25 '17 at 2:12
  • $\begingroup$ Ha, so I added a 0! okay, I will fix my numbers. $\endgroup$ – Doug M Feb 25 '17 at 2:13
  • $\begingroup$ 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 $\endgroup$ – Alex Vincent Feb 25 '17 at 2:16
  • $\begingroup$ I have $\$7,497.49$ $\endgroup$ – Doug M Feb 25 '17 at 2:17
  • $\begingroup$ Hmm apparantely the answer is still wrong $\endgroup$ – Alex Vincent Feb 25 '17 at 2:21

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