Alan Hitchcock is 37 years old today and he wishes to accumulate $519,000 by his 57 th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 37 th through his 56 th birthdays. What annual deposit must Alan make if the fund will earn 8% interest compounded annually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)
Based on the information available in the question, we can answer as follows:-
Future Value = Annual Investments * FVIFA(8%, 20 years)
Since Alan Hitchcock makes his first investment when he is 37 years old itself, we will be using the Future Value of Annuity dude to calculate the required annual investments. Hence, we will be finding the FVIFA value for 19 years and then adding 1 to it , to arrive at the correct answer.
Let annual investments be "x"
$519,000 = x * 42.44626
x = $519,000/42.44626
x = $12,227.2256
Annual Investments to be made by Alan = $12,227.23 (Rounded)
Please let me know if you have any questions via comments and all the best.
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