Answer:
- value: $66,184.15
- interest: $6,184.15
Step-by-step explanation:
The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.
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<h3>formula</h3>
The formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...
FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148
FV ≈ 66,184.15
<h3>calculator</h3>
The attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.
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<h3>a) </h3>
The future value of the annuity due is $66,184.15.
<h3>b)</h3>
The total interest earned is the difference between the total of deposits and the future value:
$66,184.15 -(12)(5000) = 6,184.15
A total of $6,184.15 in interest was earned by the annuity.
(-5,-10)E
(-5,-3)F
(-3,-10)G
The first thing any good mathematician does is convert the measurements to the same unit as what the question is asking. In this problem, it states that the pool fills at a rate of 20 cubic meters per hour. Just keep in mind that an hour is 60 minutes.
The next step is to see how many cubic meters will cost $300. This can be done by dividing 300 by 10. This gets you 30 cubic meters of water.
You already know that 60 minutes is 20 cubic meters of water. That leaves the remaining 10 cubic meters of water. By dividing the rate given, you get that 30 minutes is 10 cubic meters of water. Add the 60 and 30 together to get 90 minutes.
It will take 90 minutes for the pump to use $300.
Answer:
96
Step-by-step explanation: