document.write( "Question 1193768: A P38,000 loan bears interest at 10% compounded semi-annually and is to be repaid in semi-annual payments of P2,000 each.
\n" ); document.write( "a. How many semi-annual payments must be the debtor make?
\n" ); document.write( "b. What smaller final payment should he make six months after the last payment of P2,000 is made?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #848621 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A P38,000 loan bears interest at 10% compounded semi-annually and is to be repaid
\n" ); document.write( "in semi-annual payments of P2,000 each.
\n" ); document.write( "a. How many semi-annual payments must be the debtor make?
\n" ); document.write( "b. What smaller final payment should he make six months after the last payment
\n" ); document.write( "of P2,000 is made?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Use the standard formula for the semi-annual payment for a loan\r\n" );
document.write( "\r\n" );
document.write( "    P = ,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where L is the loan amount; r =  is the effective semi-annual compounding interest rate;\r\n" );
document.write( "n is the number of payments; P is the semi-annual payment.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In this problem  P = $2000;  r =  = 0.05.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute these values into the formula and get for semi-annual payment\r\n" );
document.write( "\r\n" );
document.write( "    2000 = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In this equation, n is the unknown: we should find n from this equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify step by step\r\n" );
document.write( "\r\n" );
document.write( "     = ,\r\n" );
document.write( "\r\n" );
document.write( "    0.052631579 = ,\r\n" );
document.write( "\r\n" );
document.write( "     = ,\r\n" );
document.write( "\r\n" );
document.write( "    1.05263158 = ,\r\n" );
document.write( "\r\n" );
document.write( "     = ,\r\n" );
document.write( "\r\n" );
document.write( "    0.95 = ,\r\n" );
document.write( "\r\n" );
document.write( "     = 1 - 0.95,\r\n" );
document.write( "\r\n" );
document.write( "     = 0.05,\r\n" );
document.write( "\r\n" );
document.write( "     = 0.05,\r\n" );
document.write( "\r\n" );
document.write( "    1.05^n = 1/0.05,\r\n" );
document.write( "\r\n" );
document.write( "    1.05^n = 20,\r\n" );
document.write( "\r\n" );
document.write( "    n*log(1.05) = log(20),\r\n" );
document.write( "\r\n" );
document.write( "    n =  = 61.4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, 61 full semi-annual payments should be made of 2,000 each,\r\n" );
document.write( "and then the last,62-th payment, should be made of the lesser amount.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  61 full semi-annual payments should be made of 2,000 each,\r\n" );
document.write( "         and then the last, 62-th payment, should be made of the lesser amount.\r\n" );
document.write( "\r\n" );
document.write( "         The total number of semi-annual payments is 62.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );