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san4es73 [151]
1 year ago
9

If you set aside $9000 at the end of each year for the next 22 years in a Roth IRA, how much will you have at your retirement 22

years from today if your IRA earns 7.8% annual percentage rate (APR) with quarterly compounding?

Mathematics
1 answer:
madam [21]1 year ago
7 0

Answer:

$501,049.37

Step-by-step explanation:

For computing the amount after 22 years we need to applied the future value which is shown in the attachment below:

Given that

PMT = $9,000

NPER = 22 years  

Annual rate = 0.078

Quarterly= 0.078 ÷ 4 = 0.0195

Effective annual rate = (1.0195^4) - 1 = 0.0803113041

Now applied the formula which is given below

= -FV(RATE;NPER;PMT;PV)

After applying the above formula, the future value is $501,049.37

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Is 16.45 greater than, less than or equal to 16.454
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A welder drops a piece of red-hot steel on the floor. The initial temperature of the steel is 2,500 degrees Fahrenheit. The ambi
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Answer: After 18.05 minutes, the temperature of steel becomes 100 degrees.

Step-by-step explanation:

Since we have given that

Initial temperature = 2500

At t = 0,

we get that

f(t)=Ce^{-kt}+80\\\\2500=C+80\\\\2500-80=C\\\\2420=C

After 2 minutes, the temperature of the steel is 1500 degrees.

so, it becomes,

1500=2420e^{-2k}+80\\\\1500-80=2420e^{-2k}\\\\\dfrac{1420}{2420}=e^{-2k}\\\\0.587=e^{-2k}\\\\\ln 0.587=-2k\\\\-0.533=-2k\\\\k=\dfrac{0.533}{2}\\\\k=0.266

So, We need to find the number of minutes when the temperature of steel would be 100 degrees.

So, it becomes,

100=2420e^{-0.266t}+80\\\\100-80=2420e^{-0.266t}\\\\20=2420e^{-0.266t}\\\\\dfrac{20}{2420}=e^{-0.266t}\\\\\ln \dfrac{20}{2420}=-0.266t\\\\-4.8=-0.266t\\\\t=\dfrac{4.8}{0.266}\\\\t=18.05

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