Finance math: find total interest rate

[939]

Homework Statement

I am given this question: what is the monthly payment necessary to ammortize a loan of $100 000 at 2.3% compounded monthly for 20 years.

I know the answer to the above: it is done by using the ammortization payment formula, in this case: R = 100 000 ((0.023/12)/(1-(1+0.023/12)))^-240.

But then it asks, "how much interest will you have paid after 20 years". Is there some algebraic way to figure this out?

Homework Equations

Loan: 100 000
Interest rate: 0.023
Time: 20 years

Not sure we need an equation.

The Attempt at a Solution

If there is no algebraic way to figure this out, I fear the only way it can be done is to draw an enormous table. Can it be done any simpler?

 

[SteamKing]

Principal + Interest = Mo. Payment * No. of payments