Problem 3. Here is a problem about your retirement. You might not think a lot about it yet (I didn't at your age), but your peers who will grow up rich are thinking about it already, and they have been for a while. I give this problem to all students in the exponential unit for Precalc, and on Assignment 1 in calculus-and-above, precisely because nobody ever talked to me about it when I was in your shoes (so I apologize if I've already given it to you in a previous course--because I keep the numbers updated, though, it's likely to be slightly different now anyway). Currently, the average annual rate of interest on Vanguard's VSMAX Gmall-cap index admiral shares fund) is 8.68% (a) Suppose that you invest $6,000 at one time this year in VSMAX, and that you stop contributing to this account afterward. If interest is compounded annually, and if the annual rate of interest stays fixed at 8.68% per year, how much money will you have in that account forty years from now? (As a good reference on compounding interest, see Section 4.1 of the OpenStax Precalculus book subsection "Applying the Compound-Interest Formula". (b) Suppose that you wait ten years before investing your $6,000. How much money will you have forty years from now in that case? (That is, how much will you have thirty years after you start investing?) (e) Suppose that beginning now, you invest $6,000 per year in VSMAX for the next fifteen years (you deposit a total of fifteen times). How much money will you deposit over that period of time? (Do not compute interest yet.) (d) Continuing the scenario in part (c), if the interest rate remains fixed at 8.68% and interest is compounded annually, how much money will be in your account after the interest is computed at the end of the fifteenth year? Hint: The amount of money in your account will be the sum of fifteen terms: 6000-10808 6000 1.0868 + 6000 1.08682 ++ 6000 - 1.0868 6000 - 1.080815 151 depot contribution 14th deposit contribution guide depois contribution You might find a tool like Wolfram Alpha useful in computing this sum; use this example as a template http://www.voltramalpha.com/input/?i-%5Cnum.%7B1%3D%7D%5E%7B20%7D+431.06%5E1, and change the numbers in it to obtain the sum above the sum is under the "Decimal Form"heading) (e) Continuing the scenario in part (d), suppose that you never make another contribution to that account Problem 3. Here is a problem about your retirement. You might not think a lot about it yet (I didn't at your age), but your peers who will grow up rich are thinking about it already, and they have been for a while. I give this problem to all students in the exponential unit for Precalc, and on Assignment 1 in calculus-and-above, precisely because nobody ever talked to me about it when I was in your shoes (so I apologize if I've already given it to you in a previous course--because I keep the numbers updated, though, it's likely to be slightly different now anyway). Currently, the average annual rate of interest on Vanguard's VSMAX Gmall-cap index admiral shares fund) is 8.68% (a) Suppose that you invest $6,000 at one time this year in VSMAX, and that you stop contributing to this account afterward. If interest is compounded annually, and if the annual rate of interest stays fixed at 8.68% per year, how much money will you have in that account forty years from now? (As a good reference on compounding interest, see Section 4.1 of the OpenStax Precalculus book subsection "Applying the Compound-Interest Formula". (b) Suppose that you wait ten years before investing your $6,000. How much money will you have forty years from now in that case? (That is, how much will you have thirty years after you start investing?) (e) Suppose that beginning now, you invest $6,000 per year in VSMAX for the next fifteen years (you deposit a total of fifteen times). How much money will you deposit over that period of time? (Do not compute interest yet.) (d) Continuing the scenario in part (c), if the interest rate remains fixed at 8.68% and interest is compounded annually, how much money will be in your account after the interest is computed at the end of the fifteenth year? Hint: The amount of money in your account will be the sum of fifteen terms: 6000-10808 6000 1.0868 + 6000 1.08682 ++ 6000 - 1.0868 6000 - 1.080815 151 depot contribution 14th deposit contribution guide depois contribution You might find a tool like Wolfram Alpha useful in computing this sum; use this example as a template http://www.voltramalpha.com/input/?i-%5Cnum.%7B1%3D%7D%5E%7B20%7D+431.06%5E1, and change the numbers in it to obtain the sum above the sum is under the "Decimal Form"heading) (e) Continuing the scenario in part (d), suppose that you never make another contribution to that account