Question

a.Your brother is saving for his daughter (3‐year‐old Monica) to start college in exactly 15 years (t=15) from today (t=0). A single year of college today (t=0) would cost him $25,000. If college costs increase at an annual rate of 3.5%, what will each year of college cost for the four years his daughter is in college (t=15 – age 18, t=16 – age 19, t=17 – age 20, and t=18 – age 21)?

b. University offers your brother the option of signing a contract to pay for all four years of college at once on the day Monica begins college (t=15 at her age of 18). What is the present value of all the college costs you calculated above (all 4 years) when Monica is 18 (t=15) if the University uses a 7% discount rate of return? Hint: Find the present value of college costs from #3 above ... you can't just add them up as they occur at different points in time on the timeline.

Answer 1

First :- Year 0 = $25,000, after it will increase at the rate of 3.5% i.e. 25,000 + 25,000*3.5/100 = 25,875

Formulae for this = P (1+r)ⁿ

Year 1 = $25,000(1.035)¹ = $25,875 like this we will reach at 15^th Year by $25000(1.035)¹⁵ So will get the amount at t=15.

Age 18(t=15) = $25,000(1.035)¹⁵ = $41,883.72

Age 19(t=16) = $25,000(1.035)¹⁶ = $43,349.65 or Smiply you can do Previous Amount(1+r)ⁿ = $41,883.72(1.035)¹ = $43,349.65

Age 20(t=17) = $25,000(1.035)¹⁷ = $44,866.89 or Simply $43,349.65(1.035) = $44,866.89

Age 21(t=18) = $25000(1.035)¹⁸ = $46,437.23 or Simply $44,866.89(1.035) = $46,437.23

Answer (a) Total Cost is sum of all year's college fees. = $176,537.49

Second :-

Now we will do present value of all the fees calculated above by using formulae PV = FV/(1+r)ⁿ

So. Age 18(t=15) will be same i.e. $41,883.72

Age 19(t=16) will be 1 Year back@ 7% on t=15 = $43,349.65/(1.07)¹ = $40,513.69

Age 20(t=17) will be 2 year back on t=15 = $44,866.89/(1.07)² = $39,188.48

Age 21(t=18) will be 3 year back on t=15 = $46,437.23/(1.07)³ = $37,906.61

There for Total for one time payment on Monica begins her college (t=15) will be $159,492.5