SOLUTION: Find how much interest ​$25,000 earns in 4 years in a certificate of deposit paying 7.5% interest compounded quarterly.

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Question 1097064: Find how much interest ​$25,000 earns in 4 years in a certificate of deposit paying 7.5% interest compounded quarterly.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

The annual interest rate is 7.5%, or 0.075.

Since interest is compounded quarterly, the quarterly interest rate is 0.075/4 = 0.01875.

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.

If the interest is compounded quarterly for 4 years, that growth factor gets applied to the beginning balance 4*4=16 times.

So the balance at the end of 4 years in your problem is
25000%281.01875%29%5E16+=+33652.86

And so the interest earned is
33652.85-25000+=+8652.86