Question 1199180
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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 = 22500
i = 0.12/12 = 0.01
n = 25*12 = 300 months (equivalent to 25 years)


Let's find the monthly payment
P = (L*i)/( 1 - (1+i)^(-n) )
P = (22500*0.01)/( 1 - (1+0.01)^(-300) )
P = 236.975431994467
P = 236.98
The monthly payment is $236.98



Verifying this result:


You can use a TVM solver such as this one
<a href = "https://www.geogebra.org/m/mvv2nus2">https://www.geogebra.org/m/mvv2nus2</a>
which emulates the TVM solver in a TI83 and TI84.


The inputs will be:
N = 300
I% = 12
PV = 22500
PMT = left blank or set to whatever you want
FV = 0
P/Y = 12
C/Y = 12
Do not type dollar signs or commas into any of the boxes.


Here's an explanation of each input:<ul><li>N = number of months in this case</li><li>I% = annual interest rate in percent form (not decimal form)</li><li>PV = present value, aka starting balance, aka loan amount</li><li>FV = 0 since we want the future value of the loan, aka final balance, to be $0 when it's all paid off</li><li>P/Y = 12 means there are 12 payments per year</li><li>C/Y = 12 means there are 12 compounding periods per year</li></ul>After the items are filled into the proper boxes, press the "Solve for PMT" button to have -236.98 show up in that box.
This value is negative to represent a cash outflow.


Here is another free online calculator you can use to verify the monthly payment:
<a href = "https://www.calculator.net/loan-calculator.html">https://www.calculator.net/loan-calculator.html</a>
There are many other options as well.


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Part (B)


The monthly payment is $236.98 found in part (A).
It is done for 300 months (aka 25 years)
This assumes no refinancing is done.


300*236.98 = 71,094


Therefore, a total of $71,094 is paid back.


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Part (C)


The previous part found that $71,094 was paid back in total.
This consists of principal, aka the amount loaned, and interest.


Divide the loan amount over this total paid back
22500/71094 = 0.31648 = 31.648% approximately
This is the percentage of the total paid toward principal.


The remaining 100% - 31.648% = 68.352% is paid toward interest.


Another way to calculate it:
interest = (amount paid back) - (principal)
interest = (71094) - (22500)
interest = 48594 dollars
percent paid interest = (interest/totalPaid)*100%
percent paid interest = (48594/71094)*100%
percent paid interest = (0.68352)*100%
percent paid interest = 68.352%
and,
percent paid principal = 100% - (percent paid interest)
percent paid principal = 100% - (68.352%)
percent paid principal = 31.648%



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Answers:


(A) Monthly payment = $236.98
(B) Total amount paid = $71,094
(C) 31.648% toward principal, 68.352% to interest
The decimal values in part (C) are approximate.
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