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Amount to be drawn from great grandfather's annuity

Problem

At the end of 1922, your great grandfather (g.g.f.) established a trust fund to be used in order to help a later generation of the family obtain a university education. The ultimate beneficiary of the trust is required to draw the trust's balance in 36 equal monthly instalments starting at the beginning of the first year in which that person commences a three year university degree course.

Your g.g.f. saved $40 per year (inclusive of 1931) until the 1932 depression left him penniless and he stopped contributing to the fund. At the end of 1948, your grandfather reactivated the trust with a single deposit of $100 out of his World War 2 service gratuity. Unfortunately, your father missed out on a university education, but he decided at the beginning of 1977, to keep the trust going via instalments of $200 per annum starting at that time and continuing right up to the date on which the trust entitlement was first paid.

Assuming you were the beneficiary of the trust as from the beginning of 2009, how much would you be able to take under the terms of the trust? The average interest rate throughout the trust's duration is j1 = 6% p.a.

Draw appropriate time-line(s) to demonstrate your calculations.

Solution Preview

See the attached file.

First calculate the balance in the fund account at the beginning of 2009
Time Line (end of the year) Amount Deposited Time in Years Till 2009 Beginning FVIF FV
1922 $40 86 150.074 $6,002.95
1923 $40 85 141.579 $5,663.16
1924 $40 84 133.565 $5,342.60
1925 $40 83 126.005 $5,040.19
1926 $40 82 118.872 $4,754.90
1927 $40 81 112.144 $4,485.75
1928 $40 80 105.796 $4,231.84
1929 $40 79 99.808 $3,992.30
1930 $40 78 94.158 $3,766.32
1931 $40 77 88.828 $3,553.13
1932 76 83.800 $0.00
1933 75 79.057 $0.00
1934 74 74.582 $0.00
1935 73 70.360 $0.00
1936 72 66.378 $0.00
1937 71 62.620 $0.00
1938 70 59.076 $0.00 ...

Solution Summary

The amount to be drawn from great grandfather's annuity is examined.

$2.19