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January 31st, 2017, 06:25 PM   #1
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Need help with a math problem

Hi. I have a word problem and I am not sure where to post because I am new. But the question is this.

A borrower on January 1st funded their loan for \$258,039.34. The rate of interest was 3.50% with an "interest only" amortization. On January 14th, just 14 days later the borrower repaid the loan in full, with a \$65 fee charged and collected as an early payment penalty.

Q: What is the actual all-in yield of return that was earned on the loan?


Help :/ I know it's more than 3.50%!

Last edited by skipjack; January 31st, 2017 at 06:41 PM.
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January 31st, 2017, 06:40 PM   #2
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Just to rewrite the question so it can be read...

A borrower on January 1st funded their loan for \$258 039.34. The rate of interest was 3.50% with an "interest only" amortization. On January 14th, just 14 days later, the borrower repaid the loan in full, with a \$65 fee was charged and collected as an early payment penalty.

What is the actual all-in yield of return that was earned on the loan?


I'm not sure all the information has been given. How often is the interest compounded?
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January 31st, 2017, 06:45 PM   #3
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It is computed on a 365/360 basis; that is, by applying the ratio of the interest rate over a year of 360 days, multiplied by the outstanding principal balance, multiplied by the actual number of days the principal balance is outstanding.
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January 31st, 2017, 06:46 PM   #4
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Did you realize that January 14th is 13 days after January 1st, not 14 days?
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January 31st, 2017, 08:27 PM   #5
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Ha! 14th day,,,
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January 31st, 2017, 10:34 PM   #6
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Work out the interest charged on the loan. If, say, that is \$325, you can calculate that the \$65 fee is a fifth of the interest amount and then increase 3.5% by a fifth to give the effective rate that you want to find. For accuracy, work to at least five significant figures.
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