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(3)zach wishes to accumulate $50,000 in a fund at the end of 20 years. if he deposits $100 + x in the fund at the end of every 3 months for the first 10 years and $100 in the fund at the end of every 3 months for the second 10 years, find x to the nearest dollar if i(4) = .04. (ans $519.79)

Respuesta :

mahamnasir

Answer:

$519.79

Step-by-step explanation:

The formula is:

[tex]PV = P (\frac{1 - ( 1 + r ) ^{-n}}{r})[/tex]

[tex](100+x)\frac{(1+\frac{0.04}{4})^{40}-1 }{\frac{0.04}{4} }(1+\frac{0.04}{4})^{40}[/tex]  [tex]+100\frac{(1+\frac{0.04}{4})^{40}-1 }{\frac{0.04}{4} }=50000[/tex]

[tex](100+x)(\frac{(1+0.01)^{40} -1}{0.01}) (1+0.01)^{40}[/tex] [tex]+(100)(\frac{(1+0.01)^{40} -1}{0.01} )=50000[/tex]

(100+x) [(1.488864 - 1) / 0.01] (1.488864) + (100) [(1.488864 - 1) / 0.01] = 50000

(100+x) [(0.488864 / 0.01)] (1.488864) + (100) (0.488864 / 0.01) = 50000

(100+x) (48.8864) (1.488864) + (100) (48.8864) = 50000

(100+x) (48.886373) (1.488864) + 4888.64 = 50000

(100+x) (72.785161) + 4888.64 = 50000

7278.5161 + 72.785161 x + 4888.64 = 50000

12167.1561  + 72.785161 x  = 50000

72.785161 x  = 50000 - 12167.1561  

72.785161 x  = 37832.8439

x = 37832.8439 / 72.785161

x = 519.787871

x = $519.79

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