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):
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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