document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=323671>Question 323671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> as a financial planner a client comes to you for investment advice after meeting with him and understanding his needs you offer him the following options option1 invest $5000 in a savings account at 6.6% interest compounded monthly option2 invest into an ordinary annunity where 1,100 is deposited each year into an account that earns 4.8% interest compounded annually. set up the formula for compound interest for option 1 and the formula for future value of an annuity for option2 in an excel spreadsheet to calculate the amount earned at the end of 6 years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #231690 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=231690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Option 1 is:\r<BR>\n" );
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document.write( "Invest $5000 in a savings account at 6.6% interest compounded monthly.\r<BR>\n" );
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document.write( "Option 2 is:\r<BR>\n" );
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document.write( "Invest $1100 each year into an annuity that earns 4.8% interest compounded annually.\r<BR>\n" );
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document.write( "What is the amount earned with each option after 6 years.\r<BR>\n" );
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document.write( "Option 1 will give you $7,421.29 at the end of 6 years which earns you $2,421.29 in interest.\r<BR>\n" );
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document.write( "That's the Future Value of $7,421.29 minus the Present Amount of $5,000.00.\r<BR>\n" );
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document.write( "Option 2 will give you $7,444.55 at the end of 6 years if you invest at the end of each time period.\r<BR>\n" );
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document.write( "Your interest earned is $7,444.55 - total payments of $6600 = $844.548084 = $844.55\r<BR>\n" );
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document.write( "Option 2 will give you $7,801.89 at the end of 6 years if you invest at the beginning of each time period.\r<BR>\n" );
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document.write( "Your interest earned is $7,801.89 - total payments of $6600 = $1201.886392 = $1201.89\r<BR>\n" );
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document.write( "The formula for the Future Value of a Present Amount is given as:\r<BR>\n" );
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document.write( "FV = PA * (1+i)^n\r<BR>\n" );
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document.write( "FV = Future Value<BR>\n" );
document.write( "PA = Present Amount<BR>\n" );
document.write( "i = interest rate per time period<BR>\n" );
document.write( "n = number of time periods.\r<BR>\n" );
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document.write( "Since you are compounding monthly, then the number of time periods = 12 * 6 = 72 and your interest rate per time period = 6.6 / 12 / 100% = .0055\r<BR>\n" );
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document.write( "Your numbers become:\r<BR>\n" );
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document.write( "FV = what you are trying to find.<BR>\n" );
document.write( "PA = 5000<BR>\n" );
document.write( "i = .00555<BR>\n" );
document.write( "n = 72\r<BR>\n" );
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document.write( "Your formula becomes:\r<BR>\n" );
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document.write( "FV = 5000 * (1.0055)^72 = $7,421.289944 = $7,421.29\r<BR>\n" );
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document.write( "Your annuity formula is a little different.\r<BR>\n" );
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document.write( "Both end of time period payment formula and beginning of time period formula are shown below:\r<BR>\n" );
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document.write( "FUTURE VALUE OF A PAYMENT WHEN THE PAYMENT IS MADE AT THE END OF EACH TIME PERIOD.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+ ALIGN=MIDDLE  ALT=\"+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "FUTURE VALUE OF A PAYMENT WHEN THE PAYMENT IS MADE AT THE BEGINNING OF EACH TIME PERIOD.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+FV%28PMT%29+=+%28%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29%29%2A%281%2Bi%29+ ALIGN=MIDDLE  ALT=\"+FV%28PMT%29+=+%28%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29%29%2A%281%2Bi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The difference between the two is that extra *(1+i) at the end of the formula for beginning of time period payments.\r<BR>\n" );
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document.write( "that represents the extra interest earned when you invest payments at the beginning of each time period rather than at the end of each time period.\r<BR>\n" );
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document.write( "FV = future value<BR>\n" );
document.write( "PMT = payment per time period<BR>\n" );
document.write( "i = interest rate per time period<BR>\n" );
document.write( "n = number of time periods\r<BR>\n" );
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document.write( "In your problem:\r<BR>\n" );
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document.write( "FV = what you want to find.<BR>\n" );
document.write( "PMT = 1100<BR>\n" );
document.write( "i = interest rate per time period = 4.8% / 100% = .048<BR>\n" );
document.write( "n = number of time periods = 6\r<BR>\n" );
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document.write( "This is because the time periods for this problem are specified in years so time periods and years are the same which means no adjustment is necessary.\r<BR>\n" );
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document.write( "Since you have all the piece parts, all you need to do is plug them into the formula.\r<BR>\n" );
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document.write( "Your formula for end of time period payments is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+ ALIGN=MIDDLE  ALT=\"+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "PMT equals 1100<BR>\n" );
document.write( "i = .048<BR>\n" );
document.write( "n = 6\r<BR>\n" );
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document.write( "The formula becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+FV%281100%29+=+%281100+%2A+%28%281.048%29%5E6-1%29%2F.048%29+ ALIGN=MIDDLE  ALT=\"+FV%281100%29+=+%281100+%2A+%28%281.048%29%5E6-1%29%2F.048%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which becomes:\r<BR>\n" );
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document.write( "FV = $7,444.548085 = $7,444.55 with payments at the end of each time period.\r<BR>\n" );
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document.write( "For investing of payments at the beginning of each time period, you take that number and multiply it by 1.048 to get:\r<BR>\n" );
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document.write( "FV = $7,444.548085 * 1.048 = $7,801.886392 = $7,801.89 with payments at the beginning of each time period.\r<BR>\n" );
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document.write( "The monthly cash flows for the Future Value of a Present Amount are shown below:\r<BR>\n" );
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document.write( "AIR = Annual Interest Rate<BR>\n" );
document.write( "NYRS = Number of Years<BR>\n" );
document.write( "CPPY = Number of Compounding Periods per Year<BR>\n" );
document.write( "CPIR  = Compounding Period Interest Rate = AIR / CPPY<BR>\n" );
document.write( "NTP = Number of Time Periods = NYRS * CPPY\r<BR>\n" );
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document.write( "TP = Time Point<BR>\n" );
document.write( "FV  = Future Value.  At TP0 this is equal to present Amount.\r<BR>\n" );
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document.write( "FV for each time Point is equal to FV for the time point before it * 1.0055.\r<BR>\n" );
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document.write( "AIR	NYRS   CPPY	CPIR	  NTP	\r\n" );
document.write( "0.066	6      12	0.0055	  72	\r\n" );
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document.write( "TP	FV\r\n" );
document.write( "0	$5,000.00\r\n" );
document.write( "1	$5,027.50						\r\n" );
document.write( "2	$5,055.15						\r\n" );
document.write( "3	$5,082.95						\r\n" );
document.write( "4	$5,110.91						\r\n" );
document.write( "5	$5,139.02						\r\n" );
document.write( "6	$5,167.29						\r\n" );
document.write( "7	$5,195.71						\r\n" );
document.write( "8	$5,224.28						\r\n" );
document.write( "9	$5,253.02						\r\n" );
document.write( "10	$5,281.91						\r\n" );
document.write( "11	$5,310.96						\r\n" );
document.write( "12	$5,340.17						\r\n" );
document.write( "13	$5,369.54						\r\n" );
document.write( "14	$5,399.07						\r\n" );
document.write( "15	$5,428.77						\r\n" );
document.write( "16	$5,458.62						\r\n" );
document.write( "17	$5,488.65						\r\n" );
document.write( "18	$5,518.83						\r\n" );
document.write( "19	$5,549.19						\r\n" );
document.write( "20	$5,579.71						\r\n" );
document.write( "21	$5,610.40						\r\n" );
document.write( "22	$5,641.25						\r\n" );
document.write( "23	$5,672.28						\r\n" );
document.write( "24	$5,703.48						\r\n" );
document.write( "25	$5,734.85						\r\n" );
document.write( "26	$5,766.39						\r\n" );
document.write( "27	$5,798.10						\r\n" );
document.write( "28	$5,829.99						\r\n" );
document.write( "29	$5,862.06						\r\n" );
document.write( "30	$5,894.30						\r\n" );
document.write( "31	$5,926.72						\r\n" );
document.write( "32	$5,959.32						\r\n" );
document.write( "33	$5,992.09						\r\n" );
document.write( "34	$6,025.05						\r\n" );
document.write( "35	$6,058.19						\r\n" );
document.write( "36	$6,091.51						\r\n" );
document.write( "37	$6,125.01						\r\n" );
document.write( "38	$6,158.70						\r\n" );
document.write( "39	$6,192.57						\r\n" );
document.write( "40	$6,226.63						\r\n" );
document.write( "41	$6,260.88						\r\n" );
document.write( "42	$6,295.31						\r\n" );
document.write( "43	$6,329.93						\r\n" );
document.write( "44	$6,364.75						\r\n" );
document.write( "45	$6,399.76						\r\n" );
document.write( "46	$6,434.95						\r\n" );
document.write( "47	$6,470.35						\r\n" );
document.write( "48	$6,505.93						\r\n" );
document.write( "49	$6,541.72						\r\n" );
document.write( "50	$6,577.70						\r\n" );
document.write( "51	$6,613.87						\r\n" );
document.write( "52	$6,650.25						\r\n" );
document.write( "53	$6,686.83						\r\n" );
document.write( "54	$6,723.60						\r\n" );
document.write( "55	$6,760.58						\r\n" );
document.write( "56	$6,797.77						\r\n" );
document.write( "57	$6,835.15						\r\n" );
document.write( "58	$6,872.75						\r\n" );
document.write( "59	$6,910.55						\r\n" );
document.write( "60	$6,948.56						\r\n" );
document.write( "61	$6,986.77						\r\n" );
document.write( "62	$7,025.20						\r\n" );
document.write( "63	$7,063.84						\r\n" );
document.write( "64	$7,102.69						\r\n" );
document.write( "65	$7,141.75						\r\n" );
document.write( "66	$7,181.03						\r\n" );
document.write( "67	$7,220.53						\r\n" );
document.write( "68	$7,260.24						\r\n" );
document.write( "69	$7,300.17						\r\n" );
document.write( "70	$7,340.32						\r\n" );
document.write( "71	$7,380.70						\r\n" );
document.write( "72	$7,421.29\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "The yearly cash flows for the End of Year Payments are shown below.\r<BR>\n" );
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document.write( "AIR = Annual Interest Rate<BR>\n" );
document.write( "CPPY = Number of Compounding Periods per Year<BR>\n" );
document.write( "CPIR  = Compounding Period Interest Rate = AIR / CPPY<BR>\n" );
document.write( "NYRS = Number of Years<BR>\n" );
document.write( "NTP = Number of Time Periods = NYRS * CPPY<BR>\n" );
document.write( "PMT = Payment per End of each Time Period\r<BR>\n" );
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document.write( "TP = Time Point<BR>\n" );
document.write( "FV  = Future Value.  <BR>\n" );
document.write( "PMT = Payment at the end of each Time Period<BR>\n" );
document.write( "TOTAL = FV + PMT\r<BR>\n" );
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document.write( "FV for each Time Period is equal to TOTAL for the time period before it * 1.048\r<BR>\n" );
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document.write( "AIR	CPPY	CPIR	NYRS	NTP\r\n" );
document.write( "0.048	1	0.048	6	6\r\n" );
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document.write( "TP	FV	        PMT	        TOTAL	\r\n" );
document.write( "0	$0.00	        $0.00	        $0.00	\r\n" );
document.write( "1	$0.00	        $1,100.00	$1,100.00	\r\n" );
document.write( "2	$1,152.80	$1,100.00	$2,252.80	\r\n" );
document.write( "3	$2,360.93	$1,100.00	$3,460.93	\r\n" );
document.write( "4	$3,627.06	$1,100.00	$4,727.06	\r\n" );
document.write( "5	$4,953.96	$1,100.00	$6,053.96	\r\n" );
document.write( "6	$6,344.55	$1,100.00	$7,444.55\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "The yearly cash flows for the Beginning of Year Payments are shown below.\r<BR>\n" );
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document.write( "AIR = Annual Interest Rate<BR>\n" );
document.write( "CPPY = Number of Compounding Periods per Year<BR>\n" );
document.write( "CPIR  = Compounding Period Interest Rate = AIR / CPPY<BR>\n" );
document.write( "NYRS = Number of Years<BR>\n" );
document.write( "NTP = Number of Time Periods = NYRS * CPPY<BR>\n" );
document.write( "PMT = Payment per Beginning of each Time Period\r<BR>\n" );
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document.write( "TP = Time Point<BR>\n" );
document.write( "FV  = Future Value.  <BR>\n" );
document.write( "PMT = Payment at the beginning of each Time Period<BR>\n" );
document.write( "TOTAL = FV + PMT\r<BR>\n" );
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document.write( "FV for each Time Period is equal to TOTAL for the time period before it * 1.048\r<BR>\n" );
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document.write( "AIR	CPPY	CPIR	NYRS	NTP\r\n" );
document.write( "0.048	1	0.048	6	6\r\n" );
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document.write( "TP	FV	        PMT	        TOTAL	\r\n" );
document.write( "0	$0.00	        $1,100.00	$1,100.00	\r\n" );
document.write( "1	$1,152.80	$1,100.00	$2,252.80	\r\n" );
document.write( "2	$2,360.93	$1,100.00	$3,460.93	\r\n" );
document.write( "3	$3,627.06	$1,100.00	$4,727.06	\r\n" );
document.write( "4	$4,953.96	$1,100.00	$6,053.96	\r\n" );
document.write( "5	$6,344.55	$1,100.00	$7,444.55	\r\n" );
document.write( "6	$7,801.89	$0.00	        $7,801.89\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "						<BR>\n" );
document.write( "The answers to your questions are:\r<BR>\n" );
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document.write( "Interest earned on Future Value of Present Amount is:\r<BR>\n" );
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document.write( "$7,421.29 minus the Present Amount of $5,000.00 = $2,421.29\r<BR>\n" );
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document.write( "The Excel Formula to use is:\r<BR>\n" );
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document.write( "=FV(0.0055,72,0,-5000,0)\r<BR>\n" );
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document.write( ".0055 is the interest rate per month.<BR>\n" );
document.write( "72 is the number of months.<BR>\n" );
document.write( "0 is the payment per month.<BR>\n" );
document.write( "-5000 is the amount invested.<BR>\n" );
document.write( "0 means payment is at the end of the time period.\r<BR>\n" );
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document.write( "Since payment equals 0, this formula is taking the future value of the amount invested.\r<BR>\n" );
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document.write( "\n" );
document.write( "Interest earned on End of Time Period Payments is:\r<BR>\n" );
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document.write( "$7,444.55 - total payments of $6600 = $844.548084 = $844.55\r<BR>\n" );
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document.write( "The Excel Formula to use is:\r<BR>\n" );
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document.write( "=FV(0.048,6,-1100,0,0)\r<BR>\n" );
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document.write( ".048 is the interest rate per year.<BR>\n" );
document.write( "6 is the number of years.<BR>\n" );
document.write( "-1100 is the payment per month.<BR>\n" );
document.write( "0 is the amount invested.<BR>\n" );
document.write( "0 means payment is at the end of the time period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Interest earned on Beginning of Time Period Payments is:\r<BR>\n" );
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document.write( "$7,801.89 - total payments of $6600 = $1201.886392 = $1201.89\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The Excel Formula to use is:\r<BR>\n" );
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document.write( "=FV(0.048,6,-1100,0,1)\r<BR>\n" );
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document.write( ".048 is the interest rate per year.<BR>\n" );
document.write( "6 is the number of years.<BR>\n" );
document.write( "-1100 is the payment per month.<BR>\n" );
document.write( "0 is the amount invested.<BR>\n" );
document.write( "1 means payment is at the beginning of the time period.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );