A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of
each year, which summation represents the money in the account 10 years after the initial deposit?
1 answer:
That is an annuity and use the attached formula.
Total = 300 * [(1.055)^11 -1] / .055 -300
Total = 300 * <span> <span> <span> 1.8020924036 </span> </span> </span> -1 /.055 -300
Total = 300 * <span>.8020924036 / .055 - 300
</span>Total = 300 * <span> <span> <span> 14.5834982473 </span> </span> </span> -300
Total = <span> <span> <span> 4375.0494741818 </span> </span> </span> -300
Total = <span>4075.05
</span>
Total = 300 * [(1.055)^11 -1] / .055 -300
Total = 300 * <span> <span> <span> 1.8020924036 </span> </span> </span> -1 /.055 -300
Total = 300 * <span>.8020924036 / .055 - 300
</span>Total = 300 * <span> <span> <span> 14.5834982473 </span> </span> </span> -300
Total = <span> <span> <span> 4375.0494741818 </span> </span> </span> -300
Total = <span>4075.05
</span>
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Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be , the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
Let equalize the resulting expression to zero and solve afterwards:
Second Derivative Test
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
The maximum sustainable yield is 202500 swordfishes.