Question 1097064
<br>The annual interest rate is 7.5%, or 0.075.<br>
Since interest is compounded quarterly, the quarterly interest rate is 0.075/4 = 0.01875.<br>
Each time interest is credited to a current amount x, the interest is 0.01875 times x, so the new balance with interest is x + 0.01875x, or 1.01875 times x.  The 1.01875 is the "growth factor" -- how much the current amount gets multiplied by each time interest is applied.<br>
If the interest is compounded quarterly for 4 years, that growth factor gets applied to the beginning balance 4*4=16 times.<br>
So the balance at the end of 4 years in your problem is
{{{25000(1.01875)^16 = 33652.86}}}<br>
And so the interest earned is
{{{33652.85-25000 = 8652.86}}}