Housing Loan Question : Principle, Interest and Repayment Structure
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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.
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.
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.
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