Stupid question

[JMM773]

Stupid question, embarressed to ask:

After a few years of making level payments, your loan naturally now has interest accrued on it. Is this total amount, interest and initial loan, considered your new outstanding principal?

A solution to a problem looked funny to me, which made me ask. I think I've just been studying for too long and might need a break

[winvicta]

Originally Posted by JMM773

After a few years of making level payments, your loan naturally now has interest accrued on it. Is this total amount, interest and initial loan, considered your new outstanding principal?

No, but you're close. What you're referring to is called the current value. The missing part is the accumulated payments. The outstanding balance is the current value minus the accumulated payments.

I hope this helps.

[ActuarialFun]

No stupid questions, that's why we are here!

[JMM773]

Originally Posted by winvicta

No, but you're close. What you're referring to is called the current value. The missing part is the accumulated payments. The outstanding balance is the current value minus the accumulated payments.

I hope this helps.

The problem in the book I was looking at has the solution exactly how you described it:

6000(1.1)^9 - x*s-angle-9 = 3x (the outstanding equals 3 times the regular payment)

My next question is when you accumulate the regular payments as they do above, don't they have the interest already calculated into them? So when you accumulate them by an s-angle calculation, isn't it like reinvesting them at the interest rate again? Or is the s-angle-9 just taking into account "Oh these payments have an interest rate of 10% in them as I'm accumulating them." Hope that makes sense

I want to clarify my understanding because I didn't pass P until I really understood the why behind some of the problems (which also helped me get through brand new questions I had never seen).

[winvicta]

Originally Posted by JMM773

The problem in the book I was looking at has the solution exactly how you described it:

6000(1.1)^9 - x*s-angle-9 = 3x (the outstanding equals 3 times the regular payment)

Originally Posted by JMM773

My next question is when you accumulate the regular payments as they do above, don't they have the interest already calculated into them?

The regular payments each valuing x are constant and remain constant throughout the calculation. So the x's themselves do not have interest built-in. It is the s-angle-n, the accumulated value of n level payments of 1, that has the accrued interest built-in. You can look at the x in the expression "x*s-angle-9" as a scaling factor; then the expression "x*s-angle-9" has the interest built-in. I think this is what you meant.

Originally Posted by JMM773

So when you accumulate them by an s-angle calculation, isn't it like reinvesting them at the interest rate again?

A simplistic answer here is yes (and re-investment at a specified rate is a very important topic down the road). At the end of a "conversion" period, the interest accrued is re-invested at the effective interest rate. Specifically, interest accrued are "converted" into principal which earns interest. This is the origin of the term "convertible". Level payments x are added to principal and earning interest by default (they need no conversion).

Originally Posted by JMM773

Or is the s-angle-9 just taking into account "Oh these payments have an interest rate of 10% in them as I'm accumulating them." Hope that makes sense.

This is also true. It says the conversion has happened exactly 9 times.

I hope I answered your questions.

[winvicta]

Originally Posted by JMM773

I want to clarify my understanding because I didn't pass P until I really understood the why behind some of the problems (which also helped me get through brand new questions I had never seen).

I agree with you 100%. The steeper the learning curve, the more gold hidden therein. I get high when I overcome one. Best of luck.