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So if anyone has been following along and wonders about Viking’s question, I have not been able to find a closed-form solution for calculating the number of payments. The equation eventually comes down to something in the form [

ax + b = c] (solve for^{x}x). If there is a solution that does not involve iteration, I don’t know of one.Wish that I could edit my posts…..

Forgot to mention that the amortization period is 36 months

p.s. Not to sidetrack the issue, but the original problem is slightly different.

In this case, I didn’t know the Total Interest Paid, but instead the Total paid; per the example above:

Total Paid= 8*$344.87+$8,460.79=$11,219.60

and I needed to find N.

However, I realized that Total Interest Paid = Total paid-Principal=$11,219.60 – $10,500= $719.60.

Thus, the two situations are basically the same.

OK. We can use the example above, strying to solve for N:

Principal=$10,500; payments/year =12; Annual Rate=11.22%; Monthly Payment Amount= $344.87; Total Interest Paid=$719.60.

Unknown: Number of Payments (N)

(From your calculator, it turns out that N=8).

However, I need the actual formula for N as a function of the known variables.

Thanks in advance!

Hi, Viking. Yes, interest is accounted for in the Balloon Payment, as it’s assumed that the Balloon Payment occurs one full payment cycle after the last Regular Payment.

As for your first question regarding Total Interest Paid after N payments, before I can answer, I need to know what the known quantities are. (I.e., do you know the interest rate? the payment amount? the length of the amortization period? etc.)

Ops, Bret you can delete my 2nd post.

I just realized what you were doing; The last month’s interest is included both in the Balloon payment and in the Total Interest Paid (this was a bit confusing)

In your case:

Total Paid= 7*$344.87+$8,805.65=$11,219.60

in my case:

Total Paid= 8*$344.87+$8,460.79=$11,219.60

End results are the same :-).

One more thing; I am a little confused about the calculator.

I input the following data:

Principal=$10,500; payments/year =12; Annual Rate=11.22%; Number of Payments= 7; Monthly Payment Amount= $344.87

The calculator shows that Total Payments= 8 and Total Interest Paid=$719.60.

To compare, I created an (Excel) amortization Table. In my table, the Total interest paid is the same as yours: $719.60 after 8 payments. However, why do I need to enter 7 payments in the calculator to get the results after 8 payments?

Furthermore, the final Balloon Payment should be the same as the remaining balance after the 8th payment, which in my case = $8,460.79 while your Calculator calculates: $8,805.65!?

Thanks again!

Hi Bret,

I wonder if you know if it possible to get a closed form equation for Total Interest Paid after N monthly payments?

There is a function for this in Excel (CUMIPMT), but I have not been able to find the equation for this.

Actually, what I am *really* after is a formula for the reverse, solving for N. In other words, I already know the Total Amount Interest Paid, but would need to calculate how many months have been paid.

TIA!!

Hi, Edna. The “minimum amortizing payment” is the smallest payment that will

eventuallypay off the loan. It’s an estimate, theoretically one penny over the interest-only payment. (The interest-only payment doesn’t reduce the principal at all, so one would never pay off the loan if only paying the interest.)Bret

Can you please explain what minimum amortizing payment means?

“Minimum amortizing payment for this Principal and Interest rate: $1977.51”.

Thank you very much. Edna