SOLUTION: Find the payment necessary to amortize a 12% loan of ​$1800 compounded​ quarterly, with 17 quarterly payments. The payment size is $?

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Question 1118312: Find the payment necessary to amortize a 12% loan of ​$1800 compounded​ quarterly, with 17 quarterly payments.
The payment size is $?

Found 3 solutions by Boreal, ikleyn, solver91311:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Payment=1800(.03)(1.03^17)/(1.03^17-1)
the .03 is the interest rate .12 divided by 4, quarterly.
round at the end
$136.71
formula is P=Ar(1+r)^n/[(1+r)^n-1]

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
I deleted my solution, since it occurred to be wrong.


Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Using the PMT function in Excel with 3% per period for 17 periods with a present value of $1800, Boreal's solution of $136.71 is correct to the penny. Ikleyn's solution of $82.72 only provides a total amount to the lender of $1406.26 after 17 payments. It would be a rare mortgage company indeed that could continue to do business in this fashion for very long.

As a check, see the following amortization table:

 Qtr 	 Pmt 	         Interest  	 Principal Red   Balance 
				                         $1,800.00 
 1 	 $(136.71)	 $54.00 	  $(82.71)	 $1,717.29 
 2 	 $(136.71)	 $51.52 	  $(85.20)	 $1,632.09 
 3 	 $(136.71)	 $48.96 	  $(87.75)	 $1,544.34 
 4 	 $(136.71)	 $46.33 	  $(90.38)	 $1,453.95 
 5 	 $(136.71)	 $43.62 	  $(93.10)	 $1,360.86 
 6 	 $(136.71)	 $40.83 	  $(95.89)	 $1,264.97 
 7 	 $(136.71)	 $37.95 	  $(98.77)	 $1,166.20 
 8 	 $(136.71)	 $34.99 	 $(101.73)	 $1,064.47 
 9 	 $(136.71)	 $31.93 	 $(104.78)	   $959.69 
 10 	 $(136.71)	 $28.79 	 $(107.92)	   $851.77 
 11 	 $(136.71)	 $25.55 	 $(111.16)	   $740.61 
 12 	 $(136.71)	 $22.22 	 $(114.50)	   $626.11 
 13 	 $(136.71)	 $18.78 	 $(117.93)	   $508.18 
 14 	 $(136.71)	 $15.25 	 $(121.47)	   $386.71 
 15 	 $(136.71)	 $11.60 	 $(125.11)	   $261.60 
 16 	 $(136.71)	  $7.85          $(128.87)	   $132.73 
 17 	 $(136.71)	  $3.98          $(132.73)	   $-   




John

My calculator said it, I believe it, that settles it


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