
Strange Loan
Jack borrows $A, over 15 months, at interest of 12% compounded monthly: 1% per month.
For the first 5 months, payment will be 10% of balance owing.
As example, if $3000 borrowed, 1st payment will be $300,
resulting in balance owing of 3000  300 + 30 = 2730;
so the next payment will be .10(2730) = $273,
resulting in balance owing of 2730  273 + 27.30 = 2484.30
For the remaining 10 months, the monthly payment will be constant
at $50 per month: the 10th $50 payment will result in a zero balance owing.
How much did Jack borrow?

Owing at month 15: $0.00
Owing at month 14: 50/1.01 = 49.50495
Owing at month 13: (49.50495+50)/1.01 = 98.51975
etc...
Owing at month 5: 473.5652
Month 5 Consideration: (473.5652 + q*0.1)/1.01 = q
Owing at Month 4: q
etc...
Alternatively:
Borrowed: A
To Be Paid in Month 1: 0.1*A
Owing at Month A: A*1.01  0.1*A = 0.91*A
It's relatively straightforward. If nothing else, a spreadsheet makes a very good tool for some problems.

Ya; but more fun to work out a general case formula:
p = .10, i = .01, m = 50, x = 5, y = 10
A = m(j  1) / (i j k)
where:
j = (1 + i)^y
k = (1 + i  p)^x

More fun that THREE different ways? I think not.
In any case, glad to see #4. (Clapping)