Using the future value formula, it is found that $100,336.67 will be available at the end of the time period, of which $40,336.67 was of interest earned.
The future value formula is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
In which:
For this problem, considering the situation described, especially the quarterly compoundings, the parameters are given as follows:
P = 1000, i = 0.065/4 = 0.01625, n = 15 x 4 = 60.
Hence the amount available is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
[tex]F = 1000\frac{(1 + 0.01625)^{60} - 1}{0.01625}[/tex]
F = $100,336.67
The amount deposited was:
15 x 4 x $1000 = $60,000.
Hence the amount earned in interest was:
$100,336.67 - $60,000 = $40,336.67
More can be learned about the future value formula at https://brainly.com/question/5025949
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