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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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9514 1404 393

Answer:

$144,205.41

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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