Question

(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)

Answer 1

$519.79

Explanation:

The formula is:

`PV = P ((1 - ( 1 + r ) ^(-n))/(r))`

`(100+x)((1+(0.04)/(4))^(40)-1 )/((0.04)/(4) )(1+(0.04)/(4))^(40)`
`+100((1+(0.04)/(4))^(40)-1 )/((0.04)/(4) )=50000`

`(100+x)(((1+0.01)^(40) -1)/(0.01)) (1+0.01)^(40)`
`+(100)(((1+0.01)^(40) -1)/(0.01) )=50000`

(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