In: Finance
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?
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 |