A person borrows $15,000 to be paid back at 5% interest (compounded) over 60 months. Makes 6 payments of $270, then borrows an additional $40,000. Makes 7 payments of $1,030, then borrows $6,000. Makes 4 payments of $1,300. How much do they owe now and can you tell me how you came up with the answer?

Question

A person borrows $15,000 to be paid back at 5% interest (compounded) over 60 months.  Makes 6 payments of $270, then borrows an additional $40,000.  Makes 7 payments of $1,030, then borrows $6,000.  Makes 4 payments of $1,300.  How much do they owe now and can you tell me how you came up with the answer?

tkhunny · Answer

What's your plan to solve this?

What tools have we?  Paper and pencil?  Calculator?  Spreadsheet? Super Computer?  Actuary?

anonymous · Answer

paper and pencil, simple calculator, and a loan calculator.  HELP!

tkhunny · Answer

Loan calculator?  Set it to "Payments at the End of the Period" and we can get started.

anonymous · Answer

Rats, I was going to cut and paste but can't.  Ok,  borrowed $15,000 in June '11.  Paid $620.  Borrowed an additional $40,000 in Jan 2012.  Paid $7,210.  In Sept borrowed an additional $6,000.  Paid $4,120.  Hence, has borrowed a total of $61,000 and has made payments totalling $11,950

anonymous · Answer

Any thoughts?  And the $620 should be $1,220.

tkhunny · Answer

Which one are we doing?  I'm tempted to start with the first one.

Set up the monthly interest factor.
$i = 0.05$
$j = i/12 = 0.05/12 = 0.0041\overline{6}$
$r = 1+j = 1.0041\overline{6}$

anonymous · Answer

Ok, so the person owes 1.00416 X the balance?

tkhunny · Answer

No.  Patience.  We need to undertand one piece at a time.

Do you understand that this is the MONTHLY interest rate factor to accumulate the balance?

tkhunny · Answer

Time - 0 Months - $15,000.00 - New Loan
Time = 1 Month - $15,000.00*r - $270.00 = $14,792.50
Time = 2 Months - $14,792.50*r - $270.00 = $14,584.14

.Do this for 6 Payments.

anonymous · Answer

Thank you so much :)!

tkhunny · Answer

Well, that's just a start.  These are sufficiently complicated that you may just have to step through them.  A spreadsheet would be ideal.

anonymous · Answer

Ok, so when I get to 6 months, I don't just add $40,000 to the balance?

tkhunny · Answer

Do be careful with "months" vs. "payments".  They will not always be the same thing.  In this case, for the first six months, that will be okay.

In other words, yes, after the 6th payment, add $40,000.00 to the balance.  After 7 more payments, add $6,000.00 to the balance.  etc.

anonymous · Answer

Correct.  Thanks again so much !