A loan is paid off in 15 years with a total of $192,000. It had a 4% interest rate that compounded monthly. What was the principal?

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  $144,205.41

Step-by-step explanation:

The relation between monthly payment A and principal P is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where the loan earns interest at annual rate r for t years. Here, the monthly payment is $192,000/(180 months) = $1066.67 /month.

Then we have ...

  P = ($1066.67)(12/0.04)(1 -(1+0.04/12)^-180) = $144,205.41

The result varies slightly depending on whether you round the monthly payment to the nearest cent. If you do that (as we have here), you find the total paid is $192,000.60 and the principal is higher by about $0.45.

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