Wikipedia:Reference desk/Archives/Mathematics/2009 April 30

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April 30

house payment

If I buy a $140,000 house with $7,000 down, $1,400/month going to the mortgage, and a one time $7,000 payment 6 months after the down payment, how many months will it take me to own the house fully if my interest rate is 4.875% fixed (no early repayment fees apply)? 65.121.141.34 (talk) 19:51, 30 April 2009 (UTC)

This could, plausibly, be a homework question, so I'm not going to give you an actual answer, but I suggest you use a spreadsheet to calculate it. Have one row for each month with the amount owed in one column and the amount paid that month in the other and another for the interest being added on. --Tango (talk) 20:06, 30 April 2009 (UTC)

Of course its a homework question. I am doing the homework before buying a house. Perhaps you could check my number. I got 113 payments (the last being lower then the standard $1400. 65.121.141.34 (talk) 20:19, 30 April 2009 (UTC)

Make that 112 since I forgot that the title line counts as 1 65.121.141.34 (talk) 20:24, 30 April 2009 (UTC)

Assuming that 4.75% is the APR compounded monthly for an effective annual rate of about 4.855%, the first $1400 payment is made 1 month after the start of the loadn, and that the $7000 payment at 6 months is in addition to the regular $1400 payment, I concur. -- Tcncv (talk) 05:24, 1 May 2009 (UTC)

I get a total of 112 payments, the last of which is $108.52. 67.122.209.126 (talk) 09:48, 2 May 2009 (UTC)

If I were you I would model this on a spreadsheet, with one row for each month. If the interest rate given is compound interest, then the monthly equivalent for the annual rate of 4.875% would be the twelveth root of 1.0487, which is 1.003974459 or about 0.3974%. I suggest having several colums for: the regular monthly payment, irregular payments (eg the $7000), the loan capital outstanding that month, the interest payable that month (which would be the previous column times 0.003974459 assuming for the sake of simplicity that your lenders recalculate it every month). The loan capital next month would be the previous months loan capital less your payments but plus the monthly interest. Creating this spreadsheet model would allow you to see the benefit of increasing the monthly payment above the minimum, if your lenders allow this. 89.242.97.56 (talk) 12:39, 3 May 2009 (UTC)

The article on present value may help to answer your question without modelling on spreadsheet. The present value of $7k downpayment is $7k. Subtract $7k downpayment and the present value of $7k 6 months later, you would get the initial balance to be paid with the regular $1.4k/month. The number of months then can be calculated using geometric series (Igny (talk) 22:58, 6 May 2009 (UTC))