Question 1200385
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Answers:<ol type="A"><li><font color=red size=3>$152.14</font></li><li><font color=red size=3>$27,385.20</font></li><li>Principal = <font color=red size=3>54.77%</font>, Interest = <font color=red size=3>45.23%</font>, these percentages are approximate.</li></ol>

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Work Shown:


Part A


Monthly payment formula
P = (L*i)/( 1 - (1+i)^(-n) )
where,
L = loan amount
i = monthly interest rate in decimal form
n = number of months


In this problem:
L = 15000
i = 0.09/12 = 0.0075
n = 15*12 = 180 months (equivalent to 15 years)


Let's find the monthly payment
P = (L*i)/( 1 - (1+i)^(-n) )
P = (15000*0.0075)/( 1 - (1+0.0075)^(-180) )
P = 152.139987624268
P = 152.14
The monthly payment is <font color=red>$152.14</font>


To check your work, you can use an online calculator such as this one:
<a href = "https://www.calculator.net/loan-calculator.html">https://www.calculator.net/loan-calculator.html</a>


Or you can use this TVM (time value of money) calculator
<a href = "https://www.geogebra.org/m/mvv2nus2">https://www.geogebra.org/m/mvv2nus2</a>
The inputs will be:<ul><li>N = 180</li><li>I% = 9</li><li>PV = 15000</li><li>PMT = leave blank</li><li>FV = 0</li><li>P/Y = 12</li><li>C/Y = 12</li></ul>After the inputs are set, press the "solve for PMT" button to have -152.14 show up in the PMT box. The value is negative to represent a cash outflow.


See this question
<a href = "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1199129.html">https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1199129.html</a>
for another example of using the TVM solver.

 
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Part B


monthly payment = $152.14 found in part A
number of months = 180  which is equivalent to 15 years


152.14*180 = <font color=red>$27,385.20</font> is the total amount paid back.


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Part C


A total of $27,385.20 is paid back.
$15,000 is the principal aka amount loaned.


(15000)/(27385.20) = 0.5477411156391
= 0.5477
= <font color=red>54.77%</font> is paid toward principal. This percentage is approximate.


The remaining percentage is toward interest.
100% - 54.77% = <font color=red>45.23%</font>



Similar question
<a href = "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1199180.html">https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1199180.html</a>
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