document.write( "Question 1205437: Lady Lee needs TZS 57,500,000 at the end of the year 2029, and her only investment outlet is a 9 percent long term certificate of deposit from Puzzo Bank (compounded biannually). With the cectificate of deposit, she makes an initial investment at the beginning of the year 2023.
\n" ); document.write( "1:What single payment could be made at the beginning of the year 2023 to achieve thi objective?
\n" ); document.write( "W:What amount could Lady Lee invest at the end of each year annually up to the ye 2029 to achieve this same objective? \n" ); document.write( "

Algebra.Com's Answer #842241 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "Lady Lee needs TZS 57,500,000 at the end of the year 2029, and her only investment outlet
\n" ); document.write( "is a 9 percent long term certificate of deposit from Puzzo Bank (compounded biannually).
\n" ); document.write( "With the certificate of deposit, she makes an initial investment at the beginning of the year 2023.
\n" ); document.write( "(1) What single payment could be made at the beginning of the year 2023 to achieve this objective?
\n" ); document.write( "(2) What amount could Lady Lee invest at the end of each year annually up to the year 2029 to achieve this same objective?
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\n" ); document.write( "\n" ); document.write( "        @Theo mistakenly determined that the deposit works 6 years.\r
\n" ); document.write( "\n" ); document.write( "        Actually, from the beginning of the year 2023 to the end of the year 2029,\r
\n" ); document.write( "\n" ); document.write( "        the deposit works and earns money 7 years (2029-2022 = 7 years).\r
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\n" ); document.write( "\n" ); document.write( "        So, I came to bring a correct solution.\r
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\n" ); document.write( "\n" ); document.write( "        I do not use an outside calculator, but make my calculations \r
\n" ); document.write( "\n" ); document.write( "        using explicit standard formulas of Financial Math with all necessary explanations.\r
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document.write( "                      Part 1.\r\n" );
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document.write( "The formula for this 7 years deposit compounded semi-annually is\r\n" );
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document.write( "    FV = ,\r\n" );
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document.write( "where X is the unknown value of the initial deposit.\r\n" );
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document.write( "From this formula,\r\n" );
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document.write( "    X =  = 31,048,439.58.\r\n" );
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document.write( "ANSWER to part 1.  The value of the one-time initial deposit is TZS 31,048,439.58.\r\n" );
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document.write( "                      Part 2.\r\n" );
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document.write( "In this part 2, the situation is close to ordinary annuity account, but there is some difference.\r\n" );
document.write( "Since the account is replenished once per year, but is compounded twice per year semi-annually,\r\n" );
document.write( "we should and can use the scheme of the annually deposited and annually compounded ordinary annuity\r\n" );
document.write( "with the EFFECTIVE annual multiplicative growth rate of   = 1.092025.\r\n" );
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document.write( "So, we use the formula for the future value of the ordinary annuity \r\n" );
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document.write( "    FV = ,   \r\n" );
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document.write( "where  FV is the future value of the account;  P is annual payment (deposit); \r\n" );
document.write( "r is the annual effective percentage rate presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years, in this case).\r\n" );
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document.write( "From this formula, you get for for the annual payment \r\n" );
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document.write( "    P = .     (1)\r\n" );
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document.write( "Under the given conditions, FV = 57,500,000;  r = 0.092025;  n = 7.  \r\n" );
document.write( "So, according to the formula (1), you get for the annual payment \r\n" );
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document.write( "    P =  = 6,211,008.91.\r\n" );
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document.write( "Answer to part 2.  The necessary annual deposit value is TZS 6,211,008.91 .\r\n" );
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\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
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\n" ); document.write( "\n" ); document.write( "The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.\r
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\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
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