compute-the-present-value-of-an-investment-that-generates-income-at-a-rate-of-5000-t-e001-t-dollars-

Name: compute the present value of an investment that generates income at a rate of 5000 t e001 t dollars
Uploaded: 2020-03-06
Duration: 3 min 11 s
Channel: Numerade
Description: Compute the present value of an investment that generates income at a rate of $5000 t e^{0.01 t}$ dollars per year forever, assuming an interest rate of $6 \%$.

Question

Compute the present value of an investment that generates income at a rate of $5000 t e^{0.01 t}$ dollars per year forever, assuming an interest rate of $6 \%$.

Alex Johnson · Accepted Answer

and this problem going to take a look at, um, a rate of 5000 t e to the 0.1 T dollars per year that&#x27;s invested forever at a rate of 6%. So are present value that we&#x27;re trying to analyze. Here is the integral from zero to infinity of 5000 Tee hee hee to the 0.0 won t times e to the power of negative 0.6 t d t. And before we analyze this improper in a girl that simplifies we have 5000 t e to the negative 0.5 t d. T. The anti derivative of this one is gonna require integration by parts. So let&#x27;s take a look at just this integral of t e to the negative 0.5 t. And, um, we&#x27;ll deal with 5000 little bit later. So let&#x27;s let you equal t, which gives us d&#x27;you equal d t and D be equal to e toothy negative through the power date of 0.5 t d t. And that gives us V equal to e to the negative 0.5 t divided by negative. 0.5 Okay. Our integration by parts formula then gives us the anti derivative um t multiplied by e to the negative 0.5 t divided by negative 0.5 minus. And then we&#x27;re gonna multiply the times, do you? That ends up giving us a plus and then the inner girl of E to the negative 0.5 t divided by 0.5 times D t. And then our anti derivative of this. We&#x27;ll get the tee times each and negatives your points, your five t and we divide that by negative 0.5 And then we do the anti derivative of this a second time, which gives us er minus e to the negative 0.5 t divided by 0.25 OK, so that&#x27;s our anti derivative. And so let&#x27;s use that now back into our improper interval. And this time we&#x27;ll make sure we include 10,000 times the limit as t goes to infinity of this anti derivative we just found. And then it&#x27;s gonna be evaluated from zero T. And so if you know if we let t go to infinity here, Uh, and we try to simplify this down. What we&#x27;re gonna get is 5000 multiplied by one over 0.25 and that value in a dollar amount is $2 million.

Brett Boyer · Answer

Okay, so the question gives us the following formula. The integral from zero to capital t of F 50 times e to the R times, the quantity capital, T minus T d t is the future value of income, and then it also gives us half of T R and Capital T and asked us to compete. So, using the formula they gave us, we get integral from 0 to 6 of 1000 e 0.4 t times e to 0.62 times six minus t duty. And this doing one simplification, we&#x27;re going to get taking out constant terms. And then distributing the exponential is together and combining the light terms, we have this constant factor of e 0.37 to allow. Then everything that&#x27;s left is a exponential factor left and the integral. And so now we just divide by the coefficient of tea and then keep the exponential term the same and evaluate so writing and out we have 8000 e to 0.372 and you&#x27;re going to divide at the front was going to be negative. Then we have 0.0 to 2 Times e to minus 0.0 to 2 t taken from 0 to 6. And so when we do that, we have approximately minus 527,000 52.9 times and then plugging in the six and zero get minus 0.124 which finally gives us a future value of approximately 65,000 $230 and 48 cents.

Amy Jiang · Answer

Okay, So you asked if I got present value for a calm pounding by some amounts. But we have a equation for that. That is P is equal to a times one plus R over em to power of Native MGI. Okay, so let&#x27;s plug in all of our variables that we know. So we know that our amounts that is 2000 our rates, that it&#x27;s 6%. So is there a 60.6 over our number of compound in periods? Since we&#x27;re calling pounding semi annually, That&#x27;s two times every year, and that&#x27;s for eight years. So two times eight. That&#x27;s 16. Okay, so let&#x27;s put this into a catheter. So that gives me a present value of 1246.33

Amy Jiang · Answer

Okay, so for us to find our present value, given that we&#x27;re calm pounding, um, by some amount, so that has an equation of P is equal to a times one, plus I to power of negative and where I is equal to our rate over are a number of compounding periods and and is equal to em. Times are number of years. Okay, so we&#x27;re given that we have and amounts of 12,820 0.77 a rate of 4.8%. And we&#x27;re compounding annually. So that&#x27;s one time every year. And that&#x27;s the power of one times six years. So plugging this into a calculator to find our present darling, he gets what he gets yet 9677 points. 13 So this was our principal or present value

Alex Johnson · Answer

this prom. We&#x27;re gonna take a look at an investment of, uh, of a rate of 10,000 e to the 0.1 tea per year forever. And we&#x27;re looking for the present value if the interest rate is 4%. So our formula for the present value is going to be integral from zero to infinity of 10,000 e toothy 0.1 t multiplied by E to zero point negative. Excuse me. Negative 0.0 for T d t. And we could simplify this slightly. So we have 10,000 e to the negative 0.3 t d t. And so for this improper interval, we have the limit as large t goes to infinity of the function 10,000 e to the negative 0.3 t divided by negative 0.3 Evaluated from zero to t. This gives us if we analyzed the limit of it. 10,000 e to the negative 0.3 large t divided by negative 0.3 minus 10,000 divided by native 0.3 And if he goes to infinity, you were left with 10,000 divided by 0.3 which is a dollar amount of 333,333 and 33 cents.

Amit Srivastava · Answer

So we have to find the but his entire future that opening to history $1000. So we know that present value open income streams mean by thirsty. Beautiful, neither. Tea party, do you? So here, Chinese in Galicia is your cousin. Your search results You were minus the explosive. Be Do you your TV? Do you want? It&#x27;s Do you? You&#x27;re in Jews, you know One by one, it&#x27;s missing movie people. 112 Do you want? Yes. 16 I find it incredible. That American girl a likeness 12 years certain sits $1 this in value. No, you can find the until just even smoking 761 suits and 46 Teoh. So that would be.

Problem

Find the volume of the solid obtained by rotating…

Problem 79 Hard Difficulty

Compute the present value of an investment that generates income at a rate of $5000 t e^{0.01 t}$ dollars per year forever, assuming an interest rate of $6 \%$.

Answer

The present value of that investment will be $\$ 2,000,000$

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The present value of that investment will be $\$ 2,000,000$

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