Calculate the future value of an annuity (when the series of payments is not uni

Question

Calculate the future value of an annuity (when the series of payments is not uniform).

1.         Calculate the future value at the end of 10 years of the following two sets of investments when the payments are received during the first five years, and the interest rate is 9%. (assume the payments are received at the beginning of each year for this problem)

                                    Investment Y                                                   Investment Z

Year 1:    $10,000                                            Year 1:          $0

                        Year 2:        7,000                                            Year 2:     $5,000

                        Year 3:        5,000                                            Year 3:      5,000

                        Year 4:        5,000                                            Year 4:      7,000

                        Year 5:             0                                              Year 5:     10,000

                                    FV of Y in year 10 = $___________              FV of Z in year 10 = $___________

Explanation / Answer

value of investment Y= 10,000(1.09)9+7000*(1.09)8+5000(1.09)7+5000(1.09)6

=21,719+ 13,948+9140+8385= $53,192

value of investment Z= 5000(1.09)8+5000(1.09)7+7000(1.09)6+10,000(1.09)5

=9962+9140+11,739+15,386

=$46,227

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