document.write( "Question 1173171: A mother wishes to set up a savings account for her son's education. She plans on investing $750 when her son is 6 months old and every 6 months thereafter. The account earns interest of 8 percent per year, compounded semiannually.
\n" ); document.write( "(a) To what amount will the account grow by the time of her son's 18th birthday?
\n" ); document.write( "(b) How much interest will be earned during this period? \n" ); document.write( "
Algebra.Com's Answer #798440 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "A mother wishes to set up a savings account for her son's education. She plans on investing $750 when her son is 6 months old
\n" ); document.write( "and every 6 months thereafter. The account earns interest of 8 percent per year, compounded semiannually.
\n" ); document.write( "(a) To what amount will the account grow by the time of her son's 18th birthday?
\n" ); document.write( "(b) How much interest will be earned during this period?
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "It is a classic Ordinary Annuity saving plan. The general formula is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV = \"P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29\",    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where  FV is the future value of the account;  P is the semi-annual payment (deposit); r is the semi-annual \r\n" );
document.write( "percentage yield presented as a decimal; n is the number of deposits (= the number of years multiplied by 2, in this case).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Under the given conditions, P = 750;  r = 0.08/2;  n = 2*18 = 36.  So, according to the formula (1), you get at the end of the 17-th year\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    FV = \"750%2A%28%28%281%2B0.08%2F2%29%5E%282%2A18%29-1%29%2F%28%280.08%2F2%29%29%29\" = \"750%2A%28%281.04%5E36-1%29%2F0.04%29\" = $58198.74.      ANSWER to (a)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Note that the mother deposits only  2*18*$750 = $27,000.  \r\n" );
document.write( "\r\n" );
document.write( "The rest 58198.74 - 27000 = 31198.74 dollars is the INTEREST what the account earns/accumulates in 18 years.    ANSWER to (b)\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On Ordinary Annuity saving plans,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );