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XYZ wants to have $192,000 in 8 years. He plants to make regular savings contributions of...

XYZ wants to have $192,000 in 8 years. He plants to make regular savings contributions of $9,400 per year for 8 years, with the first of these regular savings contributions made later today. In addition, XYZ expects to make a special savings contribution of X in 2 years. He expects to earn 13.6 percent per year. What is X, the amount fo the special savings contribution that XYZ will make in 2 years?

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Expert Solution

Year Contribution FV factor (1+13.6%)^(8-T) Future value
0 $      9,400                               2.7735 $ 26,070.81
1 $      9,400                               2.4415 $ 22,949.66
2 $      9,400                               2.1492 $ 20,202.16
3 $      9,400                               1.8919 $ 17,783.59
4 $      9,400                               1.6654 $ 15,654.57
5 $      9,400                               1.4660 $ 13,780.43
6 $      9,400                               1.2905 $ 12,130.66
7 $      9,400                               1.1360 $ 10,678.40
Total future value $139,250.29
Future value required at T8 $ 192,000.00
Future value of annual contributions $(139,250.29)
Remaining value to be accumulated from special contribution $    52,749.71
52749.71= S*(1+13.6%)^(8-2)
52749.71= S*(1+13.6%)^(8-2)
S= 52749.71/(1+13.6%)^(8-2)
S= $    24,544.27

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