1. ## 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?

2. 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 straight-forward. If nothing else, a spreadsheet makes a very good tool for some problems.

3. 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

4. More fun that THREE different ways? I think not.

In any case, glad to see #4.