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Sam takes out a bank loan for \$19500 that he will repay with 11 quarterly payments at $j_{12} = 5.75%$. Sam has some financial troubles come up and is unable to pay the 7th and 8th payments. The bank allows Sam to skip these payments and then immediately after the 8th payment the loan is refinanced at $j_{12} = 6.75%$. What is the new quarterly payment?

So I have:

$i_{1} = (1+\frac{0.0575}{12})^{3} - 1 = 0.01444399023$

$i_{2} = (1+ \frac{0.0675}{12})^{3} - 1 = 0.016970099$

$R = \frac{19500}{\frac{1-(1.0.01444399023)^{-11}}{0.01444399023}} = 1930.03$

Accumulated Value of Loan = $19500(1.01444399023)^{8} = 21870.5246$

Accumulated Value of Payments = $1930.03\frac{(1.0.01444399023)^{6} - 1}{0.01444399023} = 12006.48$

Outstanding Balance = $21870.52 - 12006.48 = 9864.04$

New quarterly payments:

$R = \frac{9864.04}{\frac{1-(1.0.016970099)^{-3}}{0.016970099}} = 3400.24$

  • 0
    Can you please format your answer using LaTex? – 2017-02-25
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    I'll help you a bit. – 2017-02-25
  • 0
    how do I do that? – 2017-02-25
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    I honestly learned LaTex through this website. I haven't edited everything but take a look at how some of it is written. – 2017-02-25
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    If you can see my edit, please tell me if its correct - for some of the fractions it was very hard to determine the order of division – 2017-02-25
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    I typed out the word *dollars* because we use the money symbol $$ for writing our phrases. – 2017-02-25
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    You can use "backslash" followed by "\$" for that e.g. \$1 – 2017-02-25
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    Yeah but when I tried closing the equations, some of them had the dollar sign to mean *the amount of money* instead of properly closing it. – 2017-02-25
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    http://www.artofproblemsolving.com/wiki/index.php/LaTeX:Symbols – 2017-02-25

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