Question

1. Your generous grandmother has just announced that she’s opened a savings account for you with a deposit of $ 10,000. Moreover, she intends to make nine more similar gifts, at the end of this year, next year, etc. If the savings account pays 8% interest, how much will you have accumulated at the end of 10 years (1 year after the last gift)? (See spreadsheet attached separately)

2. What is the present value of a series of four payments, each $1,000, to be made at the end of years 1,2,3,and 4? Assume that the interest rate is 14%

3. Anuradha Dixit just turned 55. Anuradha is planning to retire in 10 years, and she currently has $500,000 in her pension fund. Based on the longevity pattern of her family, she assumes that she will live 20 years past he retirement rate; during each of these years she desire to withdraw $100,000 from he pension fund. If the interest rate is 5% annually how much will Anuradha have to save annualy for the next 10 years? Assume that the first deposit to her pension fund will be today, followed by nine more annual deposits, and that the annual withdrawls fromage 65 will occur at the beginning of each year.

Use the following spreadsheet (the numbers are not correct) and Goal Seek to find an answer. (See spreadsheet attached separately)

4. Your annual salary is $100,000. You are offered two options for a severance package. Option 1 pays you 6 months’ salary now. Option 2 pays you and your heirs $6,000 per year forever (first payment at the end of this year). If your required return is 11% which option should you choose?

The following questions correspond to the questions above.

1. The total future value will be…?
2. The total PVs for all years is….?
3. How much is annual withdrawn at the age of 57?
4. How much is account balance at the beginning of age 84?
5. How much is the account balance at end of age 84?
6. How much is the value of alternative 1?
7. How much is the value of alternative 2?

Spreadsheets for individual questions

#1
Year Gift Future Value
0 10,000 in year 10
1 10,000 21589.24997
2 10,000 19990.04627
3 10,000 18509.3021
4 10,000 17138.24269
5 10,000 15868.74323
6 10,000 14693.28077
7 10,000 13604.8896
8 10,000 12597.12
9 10,000 11664

SUM: 145654.8746
FV FUNCTION:

#2
Interest rate 14%

Year Payment PV
1 1,000 877.1929825
2 1,000 769.4675285
3 1,000 674.9715162
4 1,000 592.0802774

Total 2913.712304
NPV function


#3
Annual desired pension payout 100,000

Annual payment 10,000

Interest rate 5%

Your age Account balance beginning of year Deposit or withdrawl beginning of year Interset earned during year Total in account end of year
55 500,000 10,000 25,500 535,500
56 535,500 10,000 27,275 572,775
57 572,775 10,000 29,139 611,914
58 611,914 10,000 31,096 653,010
59 653,009 10,000 33,150 696,159
60 696,160 10,000 35,308 741,468
61 741,468 10,000 37,573 789,041
62 789,041 10,000 39,952 838,993
63 838,993 10,000 42,450 891,443
64 891,443 10,000 45,072 946,515
65 946,515 -100,000 42,326 888,841
66 888,841 -100,000 39,442 828,283
67 828,283 -100,000 36,414 764,697
68 764,697 -100,000 33,235 697,932
69 697,932 -100,000 29,897 627,829
70 627,829 -100,000 26,391 554,220
71 554,220 -100,000 22,711 476,931
72 476,931 -100,000 18,847 395,778
73 395,778 -100,000 14,789 310,567
74 310,566 -100,000 10,528 221,094
75 221,095 -100,000 6,055 127,150
76 127,150 -100,000 1,357 28,507
77 28,507 -100,000 -3,575 -75,068
78 -75,068 -100,000 -8,753 -183,821
79 -183,821 -100,000 -14,191 -298,012
80 -298,012 -100,000 -19,901 -417,913
81 -417,913 -100,000 -25,896 -543,809
82 -543,808 -100,000 -32,190 -675,998
83 -675,999 -100,000 -38,800 -814,799
84 -814,799 -100,000 -45,740 -960,539

Solution Preview

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The following questions correspond to the questions above.

1. The total future value will be…? $156,454.87 (Problem #1)
2. The total PVs for all years is….? $2,913.71 (Problem #2)
3. How much is annual withdrawn at the age of 57? -37,411.43 (deposit, Problem #3)
4. How much is account balance at the beginning of age 84? $100,000 (Problem #3)
5. How much is the account balance at end of age 84? $0 (Problem #3)
6. How much is the value of alternative 1? $50,000 (Problem #4)
7. How much is the value of alternative 2? $ 54,545.45 (Problem #4)...

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