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QuestionCalcule o valor AA usando a fórmula A=PVA∗i1−(1+i)−nA=\frac{P V_{A}^{*} i}{1-(1+i)^{-n}} com P=40.000.000P=40.000.000, i=0,12i=0,12 e n=5n=5.

Studdy Solution

STEP 1

Assumptions1. The present value of the annuity (VA) is 40,000,000.Theinterestrate(i)is1240,000,000. The interest rate (i) is12% per period3. The number of periods (n) is54. The formula for the annuity is given by A=\frac{ V_{A}^{*} i}{1-(1+i)^{-n}}$

STEP 2

First, we need to convert the interest rate from a percentage to a decimal.
12%=0.1212\% =0.12

STEP 3

Now, plug in the given values into the annuity formula.
A=40,000,000∗0.121−(1+0.12)−5A=\frac{40,000,000 *0.12}{1-(1+0.12)^{-5}}

STEP 4

Calculate the value of the denominator.
1−(1+0.12)−=1−(1.12)−1-(1+0.12)^{-} =1 - (1.12)^{-}

STEP 5

Calculate the value of (1.12)−5(1.12)^{-5}.
(1.12)−5=0.5674(1.12)^{-5} =0.5674

STEP 6

Subtract the calculated value from1.
1−0.5674=0.43261 -0.5674 =0.4326

STEP 7

Now, calculate the value of the numerator.
40,000,000∗0.12=4,800,00040,000,000 *0.12 =4,800,000

STEP 8

Now, divide the numerator by the denominator to find the value of A.
A=4,800,0000.4326A = \frac{4,800,000}{0.4326}

STEP 9

Calculate the value of A.
A=4,800,000.4326=11,099,631.18A = \frac{4,800,000}{.4326} =11,099,631.18So, the value of the annuity A is approximately $11,099,631.18.

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