Question

2. You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount. (You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child's education? ( Use excel and show functions)

Answer 1

Future value = present value*(1+ rate)^time

Future value = 10000*(1+0.05)^10

Future value = 16288.95

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-10000

I/Y =5

N =10

PMT = 0

CPT FV

Using Excel

=FV(rate,nper,pmt,pv,type)

=FV(0.05,10,,-10000,)

PV Annuity due= C/((r-g)/100)*(1-((1+g/100)/(1+r/100))^n)*(1+r/100)

C = First cash flow

i = interest rate g = growth rate

n = number of payments

PV= 16288.95/((6-5)/(100))*(1-((1+5/(100))/(1+6/(100)))^(4))*(1+6/(100))

PV = 64239.57

FVAnnuity Due = c*(((1+ i/100)^n - 1)/i)*(1 + i/100)

C = Cash flow per period

i = interest rate

n = number of payments

64239.57= Cash Flow*(((1+ 6/100)^10-1)/(6/100))*(1+6/100)

Cash Flow = 4597.85

Using Calculator : Press buttons : "2ND"+"PMT"+"2ND"+"ENTER"+"2ND"+"CPT" then assign

FV =64239.57

I/Y =6

N =10

PV = 0

CPT PMT

Using Excel

=PMT(rate,nper,pv,fv,type)

=PMT(6/(100),10,,64239.57,1)