# Housing Loan Question : Principle, Interest and Repayment Structure

A housing loan is taken out for $250,000. The rate of interest is 6% per annum and the loan is over a 25 year period. The repayments are made monthly.

The formula:

(See attached)

gives An the amount owing at the end of the nth time period. Here n is given in months and r, expressed as a decimal, is the monthly rate of interest on the loan. P is the monthly repayment and A is the amount borrowed.

1) Calculate P for the above data

2) Calculate amount owing on the loan after 10 years

3) At end of 10 years the house buyer inherits $80,000 which he pays off the loan. Assuming that he continues to make the same monthly repayments, calculate how many months before the loan is fully paid off.

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#### Solution Preview

From the condition, we know

A=$250,000, r=0.06/12=0.005, 25 years is 25*12=300 months.

At the end of the 25 years or 300 months, A(n)=0.

Thus we can find P.

1) ...

#### Solution Summary

Questions relating to a housing loan relating to principle, interest and repayment structure are answered in detail.