Question & Answer: A graduating senior decides to take a year off and work to save money for college. The student plans to invest all money e…..

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A graduating senior decides to take a year off and work to save money for college. The student plans to invest all money earned in a savings account earning 6% interest, compounded quarterly. The student hopes to have $5000 by the time school starts in 12 months. How much money will the student have to save each month? Sketch the cash flow diagram. A) $396/month B) $405/month C) $407/month D) $411/month The Powerball Lottery, worth $182 million, was won by a single individual. The winner was given two choices: receive 26 payments of $7 million each with the first payment to be made immediately and the rest to be made at the end of each of the next 25 years, or receive a single lump-sum payment now that would be equivalent to the 26 payments of $7 million each. If the state uses an interest rate of 4% per year, calculate the amount of the lump sum payment.

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Principle Addition Total Interest closing
405.00 0.00 405.00 0.00 405.00
405.00 405.00 810.00 0.00 810.00
810.00 405.00 1215.00 18.23 1233.23
1233.23 405.00 1638.23 0.00 1638.23
1638.23 405.00 2043.23 0.00 2043.23
2043.23 405.00 2448.23 36.72 2484.95
2484.95 405.00 2889.95 0.00 2889.95
2889.95 405.00 3294.95 0.00 3294.95
3294.95 405.00 3699.95 55.50 3755.45
3755.45 405.00 4160.45 0.00 4160.45
4160.45 405.00 4565.45 0.00 4565.45
4565.45 405.00 4970.45 74.56 5045.00

Bonus

Year Amount PVF@4% DCF
0 7 1.000 7.000
1 0 0.962 0.000
2 7 0.925 6.475
3 7 0.889 6.223
4 7 0.855 5.985
5 7 0.822 5.754
6 7 0.790 5.530
7 7 0.760 5.320
8 7 0.731 5.117
9 7 0.703 4.921
10 7 0.676 4.732
11 7 0.650 4.550
12 7 0.625 4.375
13 7 0.601 4.207
14 7 0.577 4.039
15 7 0.555 3.885
16 7 0.534 3.738
17 7 0.513 3.591
18 7 0.494 3.458
19 7 0.475 3.325
20 7 0.456 3.192
21 7 0.439 3.073
22 7 0.422 2.954
23 7 0.406 2.840
24 7 0.390 2.731
25 7 0.375 2.626
26 7 0.361 2.525
Lump Sum Payment 112.165

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