# Compound interest question?

Asked by skfinkel (12611 ) 3 months ago

Is there a formula for compounding a principal amount when the principal is being paid off over five years? The formulas I am finding just assume the principal stays the same—or is that the way it is done until it is paid off?
I did find an answer for just compounding—so that I have. The question is, is there a different formula if the amount is less each month? or is that already taken in to consideration?

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Most payment schedule pay both interest and principal each month. I’ve never heard of compounding principal. I have a couple of amortization formulas in the office.

This is a debt, not a house. So maybe that’s the difference. It was calculated to be paid off in five years, but the interest was not included. And that is to be compounded interest.

skfinkel (12611 )

No, it’s not a difference. A debt is a debt. Interest on debts isn’t usually compounded, it’s simple interest. (NYS law). Your state may allow rule of 78’s or some other form, so I’d have to know the formula.
Edit: Is it imputed interest?

A debt is a debt. Interest on debts isnâ€™t usually compounded,

Credit cards compound interest on interest, no? They add the interest to the total debt, and calculate interest on the new total.

jaytkay (21445 )

@jaytkay Credit cards are different, they play by some mean rules. I was trying to figure out what kind of debt skfinkel was referring to.

I don’t even understand compounding a principal? The principal gets paid down. Interest rates are compounded on things like savings accounts.

Some debts the initial payments are front loaded with higher interest and very little principal being paid off. Maybe that is what you are talking about. Home mortgages are usually like this.

JLeslie (42517 )

Yes there is a formula. It differs depending on whether your interest is continuously compounded or compounded in discrete intervals, like every month. Which are you looking for?

Mariah (17700 )

May as well post them both…

If your interest is continuously compounded:
A = Pe^(rt)
Where A is the balance, P is the starting principle, e is the mathematical constant e (~2.718), r is the interest rate in decimal form (so if 1%, use .01), and t is the time period you’re looking for, i.e. change in 1 year. Make sure to use the same units of time in r and t! That is, if r is the annual rate, t needs to be time in years.

If your interest is compounded in discrete intervals:
A = P(1 + r/n)^(nt)
Where A, P, r, t are as above, and n is the number of times in one time unit (again make sure you’re using consistent time units) that the interest is compounded.

Mariah (17700 )

Mariah, I think it would be every month. And the period would be for five years, so sixty times.

skfinkel (12611 )

Oops! I was a little too hasty. Okay! So in your case, you’re using the second formula.

A = P(1 + r/12)^(12*5) – just fill in your starting principle and interest rate for P and r respectively.

Mariah (17700 )

Thank you!

what is ^?

skfinkel (12611 )

Exponent. No prob. :)

Mariah (17700 )

oh, thanks. It’s been quite a while!

skfinkel (12611 )

Oh hold on. I read too quickly. Because this is something you’re paying down, not up, make sure to use a negative value for r (usually this formula is used to calculate interest earned in bank accounts, a rising balance). So just slap a negative sign in front of whatever you were going to use for r. That should do it.

Mariah (17700 )

ok…thanks again.

skfinkel (12611 )

or