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The function f(x)=1200 represents the rate of flow ofmoney in dollars per year. Assume a 20-year periodat 5% compounded continuously. Find (A) thepresent value, and...

Question

The function f(x)=1200 represents the rate of flow ofmoney in dollars per year. Assume a 20-year periodat 5% compounded continuously. Find (A) thepresent value, and (B) the accumulated amount of moneyflow at t=20.

The function f(x)=1200 represents the rate of flow of money in dollars per year. Assume a 20-year period at 5% compounded continuously. Find (A) the present value, and (B) the accumulated amount of money flow at t=20.



Answers

Each of the functions represents the rate of flow of money in dollars per year. Assume a 10 -year period at 8$\%$ compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at $t=10$ .
$$f(t)=0.05 t+500$$

This problem were given a 10 year period interest rate of 8% and function F F T equals 25 teeth and were asked to find the present value on the accumulated amount of money flow after a 10 year period to find the present value, we're going to use the equation. P equals the integral fft e to the negative rt DT from zero to capital T t is going to be our 10 year period. F of tea is our function 25 tea and our is our interest rate of 8%. Next, we're gonna plug in everything we know after playing in our known values. This is what your equation should look like. Next. We're going to evaluate the integral for our present value. One simplified, you should end up with the present value of $746.91. Next, we're gonna find the ACU 1,000,000 amount of money flow after a 10 year period. To do so, you're going to use this equation A equals eased to the our capital teeth times the integral f of T e to the native rt DT from zero to capital t over variables in this equation of the same? Uh huh. Relation as in the previous equation, we're gonna go ahead and plug in all of our numbers. This is what your creation should look like once all the numbers are plugged in. Then we're gonna go ahead and evaluate this for a one. Simplified, your accumulated amount of money flow A should equal $1662 in 27 cents.

This question were asked for the present value on the accumulating amount of money after a 10 year period of time. So this is the equation we're gonna use to find the present value where T is our period Given or 10 FFT is gonna be 500 and other rate is 0.8. Next, we're gonna plug all that in. So this is what you're gonna get whenever everything is plunging. Next year is gonna take the integral. I want to take the integral and evaluate should end up with a president about you. 3441.69 Next, we're going to find the accumulated amount of money to do this. We're going to use the equation equals the integral of F 50 DT from zero to t, and we're gonna fill in 10 for tea and 500 for half of tea. Next, we're going to evaluate this any role. Once you evaluate the integral, you should end up with accumulated value of 5000

In this problem. We are given a function the amount of interest in the time period and were asked to find the present value in the accumulated amount of money flow after that time period to find the present value, Rania's the formula p who is the integral of f of t e to the negative rt DT from zero to Capital T where capital T it's going to be our time period or 10 and then our is going to be our rate or 8% f of t is going to be equal to 500. Next, we're just gonna plug in everything that we know. This is what your equation should look like once you plug in everything we know, and then we're just going to evaluate that for the present value. So once you evaluate, you should end up with a present value of 3441 dollars in 69 cents. Next, we're gonna find the accumulated amount of money flow. After 10 years to do that, we're going to use the formula a close e to the R capital T times the integral of f f T e to the negative rt DT from zero to Capital T. In this formula, all of our symbols mean the same as what they did in the previous our equation. So what we're gonna do now is plug in everything we know. This is what your equation should look like after everything is plugged in. Then we're just going to evaluate that for a So once you evaluate the integral and multiply everything together, we should get an accumulate amount of money flow of $7659 in 63 cents.

This problem were given a 10 year period at an 8% interest rate and were asked to find the president value and the accumulate amount of money flow after that 10 year period were also given the function. The first thing we're gonna do is used the equation p equals the integral fft e to the negative rt DT from zero to capital T to find the present value. Your capital t is our period or 10 years f of t is going to be our function given and our is going to be our rate of 8%. Next, we're gonna plug in everything we know. This is what your equation should look like once you plug everything in and just a note these to use their exponents, we're going to add together. Next. We're just going to evaluate that integral. Once you evaluate the integral, you should end up with the present value of $32,968.40. Next, we're gonna find the accumulate amount money flow after 10 years To do this, you're going to use the equation A equals e to the R capital T times the integral effort t e to the negative r t d t from zero to capital t this equation, all of our symbols mean the same as they did in the previous equation. Now we're gonna go ahead and fill in everything we know. So this is what it should look like. Once you plug everything in once again to ease here, their exponents will add together, and then we're just going to evaluate this. So once you simplify that, you should end up with an accumulate amount of money flow $73,372.40.


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