Weird loan!

Feb 2015
2,255
510
Ottawa Ontario
A $1000.00 loan over a 12month period, at rate 1% per month.
Monthly payments are p per month for 1st 4 months,
no payments next 4 months, then p per month for last 4 months.
Code:
MONTH PAYMENT INTEREST BALANCE 
  0                    1000.00 
  1     -p     10.00     ? 
  2     -p       ?       ? 
  3     -p       ?       ? 
  4     -p       ?       ? 
  5     0.00     ?       ? 
  6     0.00     ?       ? 
  7     0.00     ?       ? 
  8     0.00     ?       ? 
  9     -p       ?       ? 
 10     -p       ?       ? 
 11     -p       ?       ? 
 12     -p       ?      0.00
Calculate p.
 
Feb 2015
2,255
510
Ottawa Ontario
Yepper! 133.23801887...

I equated FV's.
What method did you use?
 
Jun 2013
1,134
605
Lebanon
I used the formula

\(\displaystyle 1000 \frac{r^{12}(r-1)}{\left(r^8+1\right)\left(r^4-1\right)} \)

where $r=1.01$
 
Feb 2015
2,255
510
Ottawa Ontario
Nice!

a = 1000
i = .01

r = 1 + i
k = (r^4 - 1) / i

a*r^12 = p(k*r^8) + p*k
ar^12 = p(kr^8 + k)
p = ar^12 / [k(r^8 + 1)]