You are saving for the college education of your two children. They are two year

Question

You are saving for the college education of your two children. They are two years apart in age; one will begin college 14 years from today and the other will begin 16 years from today. You estimate your children's college expenses to be $35,000 per year per child, payable at the beginning of each school year. The annual interest rate is 6.5 percent. Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college. How much money must you deposit in an account each year to fund your children's education? (Do not round intermediate calculations and round your answer to 2 decimal places, g,32.16.) Annual savings

Explanation / Answer

expense at the end of 14 years , x1 = $35,000

expense at the end of 15 years , x2 = $35,000

expense at the end of 16 years , x3 = $35,000 ( child 1) + 35,000 (child 2) = 70,000

expense at the end of 17 years , x4 = $35,000 +35,000 = $70,000

expense at the end of 18 years , x5 = $35,000

expense at the end of 19 years , x6 = $35,000

interest rate , r = 6.5% = 0.065

value of these expenses at the end of 14 years from today, z = x1 + (x2/(1+r)) + (x3/(1+r)2) + (x4/(1+r)3) + (x5/(1+r)4) + (x6/(1+r)5)

= 35000 + (35000/(1.065)) + (70000/(1.065)2) + (70000/(1.065)3) + (35000/(1.065)4) + (35000/(1.065)5)

= 35000 + 32863.8498 + 61716.1498 + 57949.4364 + 27206.3082 + 25545.8293

= 240281.573

value of these expenses today = v = z/(1+r)14 = 240281.573 /(1.065)14 = $99500.6593

no. of deposits to be made , n = 16

let the annual deposit to be made each year = A

v = A*PVIFA(16,6.5%)

where PVIFA = present value interest rate factor of annuity

PVIFA(16,6.5% ) =[ (1+r)n -1]/((1+r)n *r)

= [ (1.065)16 -1]/((1.065)16 *1.065) = 9.767764183

v = A*9.767764183

A = v/9.767764183 = 99500.6593/9.767764183 = $10,186.63611 or $10,186.64 ( after rounding off)

annual savings = A = $10,186.63611 or $10,186.64 ( after rounding off)

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