Question

You are saving for your child's education since you did not participate in the Texas Tomorrow Fund. Your child is five-year-old today. Starting next quarter, you will deposit $300 every quarter until you child turns 17. Your last payment will be on his 17th year. You can to withdraw $X very year starting his 18th birthday for 4 years, first payment on his 18th birthday. Assuming you have investing your money in an account is provides 12% return and the interest is compounded daily (365 days).

a. $13,826.63

b. $11,998.78

c. $10,608.75

d. $8,982.45

e. $5,782.88

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+12/365*100)^365-1)*100

Effective Annual Rate% = 12.7475

We need to convert effective rate to quarterly rate as deposits are made on quarterly basis

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

12.7475 = ((1+Stated rate%/(4*100))^4-1)*100

0.127475=((1+Stated rate%/(4*100))^4-1)

1.127475=(1+Stated rate%/(4*100))^4

1.127475^(1/4)=(1+Stated rate%/(4*100))

1.03044=(1+Stated rate%/(4*100))

0.03044=Stated rate%/(4*100)

stated rate% = 0.03044*4*100

stated rate=12.1798%

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

FV= 300*(((1+ 12.1795/400)^(12*4)-1)/(12.1795/400))

FV = 31721.09

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

31721.09= Cash Flow*((1-(1+ 12.7475/100)^-4)/(12.7475/100))

Cash Flow = 10608.75

FVordinary Annuity

PVordinary Annuity

FVordinary Annuity

PVordinary Annuity