John and Daphne are saving for their daughter Ellen\'s college education. Ellen

Question

John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). So far, John and Daphne have accumulated $15,000 in their college savings account (at t =0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs? a. $1,965.21 b. $2,068.64 c. $2,177.51 d. $2,292.12 e. $2,412.76 I really need to know how you came up with the answer...so could you please give a step by step explanation

Explanation / Answer

Ok first of all you have to find the present value of all of your future liabilities and savings your tuition liabilities will be (present valued at t=7) (14.5)*(1.035^8)/1.09 + (14.5)*(1.035^9)/1.09^2 + (14.5)*(1.035^10)/1.09^3 + (14.5)*(1.035^11)/1.09^4 =17.51718 + 16.63329 + 15.79399 + 14.99705 =64.94151 or $64941.51 now we need the present value of all of your savings (at t = 7) for your 15000 (15000)*(1.09^7) = 27420.5868 now for all of your 5000 installments we present value each installment with a different exponent so we have 4 payments of (5000)(1.09^6) = 8385.50 (5000)(1.09^5) = 7693.11 (5000)(1.09^4) = 7057.91 (5000)(1.09^3) = 6475.14 if we add all of our savings we'll have at t=7 57032.25 now we have to find algebraically the value of the 3 equal payments which will equal the difference between our liabilities and our savings at t=7 the difference being 64941.51 - 57032.25 = 7909.26 the equation for which can be written as: (x)(1.09^2) + (x)(1.09) + x = 7909.26 3.2781 x = 7909.26 x = 7909.26/3.2781 =2412.75739 or simply e. 2412.76 Report Abuse

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