A company plans to invest X at the beginning of each month in a zero-coupon bond in order to accumulate 100,000 at the end of six months. The price of each bond as a percentage of redemption value is given in the following chart:1 2 3 4 5 6 ; 99% 98% 97% 96% 95% 94%; Calculate X given that the bond prices will not change during the six-month period.

x = $16,078.46

Explanation:

$100,000 = 1.0101x + 1.0204x + 1.0309x + 1.0417x + 1.0526x + 1.0638x

$100,000 = 6.2195x

x = $100,000 / 6.2195 = $16,078.46

month               investment              value at end of month 6

1                         $16,078.46                    $17,104.74

2                        $16,078.46                    $16,924.68

3                        $16,078.46                    $16,748.39

4                        $16,078.46                    $16,575.73

5                        $16,078.46                    $16,406.59

6                        $16,078.46                    $16,240.87

total                  $96,470.76                     $100,001*

*the extra $1 is due to rounding errors.

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