document.write( "Question 1110313: Hi\r
\n" ); document.write( "\n" ); document.write( "tom buys a house for 210,000 dollars pays a 60,000 deposit and then pays off the balance at 950 dollars per month 25 years.\r
\n" ); document.write( "\n" ); document.write( "find the yearly interest paid and the interest rate charged\r
\n" ); document.write( "\n" ); document.write( "thanks \n" ); document.write( "
Algebra.Com's Answer #725391 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
The monthly payment for a mortgage is calculated using the following formula,
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\n" ); document.write( "M = Pi/[q(1-[1+(i/q)]^-nq)], where M is the monthly payment, P is the principal amount being financed, i is the interest rate, q is the number of payments per year and n is the number of years
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\n" ); document.write( "for this problem, M = $959, P = $210,000 - $60,000 = $150,000, q = 12, n = 25
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\n" ); document.write( "the equation becomes
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\n" ); document.write( "950 = 150000i/[12(1-[1+(i/12)]^-300)]
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\n" ); document.write( "The interest rate i can't be solved for algebraically - it must be found numerically.
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\n" ); document.write( "(1) Try a value i1 for i. A reasonable guess that will be too high is the interest rate for simple interest, i1 = Mnq/P - 1.(i1 = 950(300)/150000 = 0.9
\n" ); document.write( "(2) Using that, compute the principal P1 for that rate. If P1 < P, then the interest rate i1 > i, but if P1 > P, then i1 < i.
\n" ); document.write( "P1 = M[q(1-[1+(i/q)]^-nq)]/i
\n" ); document.write( "P1 = 950[12(1-[1+(0.9/12)]^-300)]/0.9
\n" ); document.write( "P1 = 12666.67
\n" ); document.write( "(3) Using the fact from (2), try another interest rate i2 and compute the corresponding principal value P2.
\n" ); document.write( "let i2 be 0.07
\n" ); document.write( "P2 = 950[12(1-[1+(0.07/12)]^-300)]/0.07
\n" ); document.write( "P2 = 134412.55
\n" ); document.write( "(4) Then try the new rate,\r
\n" ); document.write( "\n" ); document.write( " i3 = (i1[P2-P]+i2[P-P1])/(P2-P1)\r
\n" ); document.write( "\n" ); document.write( "(5) Replace the worse of the two starting interest rates with this new rate i3.\r
\n" ); document.write( "\n" ); document.write( "Repeat steps 4 and 5, always using the two interest rates with the corresponding principals closest to P as i1 and i2. Continue until you have found an interest rate such that the corresponding principal when rounded to the nearest cent gives P. Then i is equal to that interest rate.
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\n" ); document.write( "carry out this series of repetitions
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\n" ); document.write( "Note that i = 5.81% yields a principal of $150141.30
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