Principal Payment

[Keebs]

I am struggling with the last part (c) the following question:

Company A borrowed $80,000 for new equipment at 8% per year compounded quarterly. It is to be paid back over 3 years in equal quarterly payments. Calculate a) HOw much interest is in the sixth payment? b) How much principal is in the sixth payment? and c) What principal is owed immediately following the sixth payment?

I determined that the interest and principal on the 6th payment are $979.18 and $6,585.59. However, I am completely stumped on how to determine a principal payment immediately after the 6th payment is paid and no interest accrued. I have tried using the PPMT in excel and long hand calculations using interest tables, but I am getting numbers that I know are not correct. Can someone help me please?

 

[tkhunny]

You must first make up the right question. Try this one: "Immedaitely after the sixth payment, what is the remaining principal balance?"

 

[Keebs]

Well the total balance after the 6th payment is $42,373.52, but I dont know how to determine the principal balance when you dont consider interest. I tried using an excel calculation(PPMT(0,7,12,-80,000)) using 0%, but with that formula I get $6,666.67. If I change the term I still get $6,666.67. I guess I still dont know how to think of this properly.

 

[Denis]

Well the total balance after the 6th payment is $42,373.52, ......

The question is: "What principal is owed immediately following the sixth payment?"

Answer: simply $42,373.52
Same as if you borrowed that amount, over 6 quarters (the last 6 quarters), at same rate.

 

[JeffM]

Well the total balance after the 6th payment is $42,373.52, but I dont know how to determine the principal balance when you dont consider interest. The balance IS the remaining principal due (unless you have defaulted). I tried using an excel calculation(PPMT(0,7,12,-80,000)) using 0%, but with that formula I get $6,666.67. Which is the right answer. 80,000 / 12 = 6,666.67. If the interest rate is zero, the sum of the periodic payments will equal the initial principal because no interest is involved. By setting the rate to zero, you have eliminated the factor that makes the problem somewhat difficult. Never use zero as the interest rate if you are trying to understand financial formulas. If I change the term I still get $6,666.67. You must have changed the 7, not the 12. This whole problem is about a series of identical payments so the total payment in period 8 will inevitably be the same as the total payment in period 7. And of course if the interest rate is zero, the total payment will all be principal, which will then be the same in every period. I guess I still dont know how to think of this properly.

Does your book give you algebraic formulas? The excel formulas will save you time, but they do nothing to teach you the logic behind them. You will never be absolutely sure if you are using the right one. If you derive the algebraic formulas (that is, see why they work) you will grasp the logic and THEN can use the excel formulas with understanding. If you do not have algebraic formulas or cannot derive them on your own, come back and talk some more.