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# Word Problems/Interest Rate

Question
I have found that you answered this question before, but you didn't specify how you found the interest rate without it given.
In the other question similar to mine, the interest rate was given, but i have to explain in my writing assignment how i found the interest rate and i don't understand how to find it. "Interest rate is 5.75 and compounding period monthly." was given.

Pretend that you are a financial consultant. A person comes into your office and says that he wants to buy his first home and wants your sage analysis of his situation.
He can afford \$1030 per month toward his mortgage, which we will assume has a term of 30 years. He can make a down payment of \$27,000. He wants to know the following:
What is the highest-priced house he can afford?
How much interest will he pay over the entire duration of his mortgage, assuming that he makes every payment on time and does no early paying down of the principal?
Ten years into the mortgage, how much would he have to pay in one lump sum to retire the debt?
You must compose a written reply to this person answering those questions and clearly explaining how you got those answers. Display your expertise at analyzing mortgages. Do not use a "mortgage calculator" or similar computer software (on the Internet or anywhere else) that does the work for you. When you use a formula, first state it in its general form, with no value substituted for any variable; then show it with values substituted. You must explain what the symbols in it mean. When you substitute specific values into a formula, you must explain why the variables have those values.

The loan is for 30 years, every month, so there are 30*12=360 periods.

The interest per year is 5.75%, so per month it is this value over 12.

To get the future value given the present value, multiply by (1+i)^n where i is the interest rate and n is the number of periods.  For the whole loan, this was said to be 360.

The formulas used involve P = present value, F = future value, and A = annuity.

The relation between P and F is F = P(1+i)^n, where i is the interest and n is the number of periods.  The relation between F and A is F = A((1+i)^n - 1)/i), for that’s the standard annuity formula.  Note that in mathematics, (1+i) is raised to the n and then 1 is subtracted from that, and then that is divided by i.  F/P is given and F/A is given as well.  P/F is just the reverse of F/P.

The annuity for this loan is A = \$1,030 each month.

The highest price house is \$204,345.  This is found by taking the payment of \$1,030, using F/A to compute the future value, using P/F to compute the present value, and then adding on the original down payment.

To compute the total paid in interest, compute the total payment minus the initial price.  That is, there would be 360 payment of \$1,030 and the original loan is the price of the house minus the original payment.

That is, 360*1030 – (204,345 – 27,000) = \$193,455.
After 10 years, only \$28,957 will be paid off.
This will leave \$148,207 left on the principal.

From what I see, this is really close to right, but I haven't done problems like this since before the year 2000.

Word Problems

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#### Scott A Wilson

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I have answered every question that was a story problems that had any relation to math for which an answer existed. I have ever answered some questions which had a vague relation to math, but still related.

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