Question

1. Jackie and Joe have just had their first baby and they wish to insure that enough money will be available to pay for their daughter's college education. Assume that the educational savings account will return a constant APR of 9%. They have initial savings of $4358 deposited into the account right away (on the day the child was born) and plan to make further deposits into the educational savings account on each of their daughter's birthdays, starting with her first birthday and ending on her 18th birthday. They have a savings goal in the amount of $50335 will be needed for college by their daughter’s 18th birthday.

a. If the couple is to make an equal deposit into the account every year (annual compounding interest), how much do they need to deposit to reach the savings goal in the amount of $50335 in 18 years? (Enter dollar and cents amount, for example, enter $20.06 as 20.06, ignore the +/- sign.)

b.If the couple does not have any initial savings and still plans to accomplish the same savings goal in the amount of $50335 in 18 years by making an equal deposit into the account every year (annual compounding interest), how much do they need to deposit to reach the savings goal in the amount of $50335? (Enter dollar and cents amount, for example, enter $20.06 as 20.06, ignore the +/- sign. )

c. If the couple accomplishes the goal in the amount of $50335 by their daughter’s 18th birthday, what is the maximum their daughter can withdraw from the account every year over the 4 years she will be in college if she withdraws an equal amount each year? Assume the interest rate remains 9% and the annual withdrawal occurs at the end of each year after she enters college. (Enter dollar and cents amount, for example, enter $20.06 as 20.06, ignore the +/- sign. )

Answer 1

1. a) Rate =9%
Number of Years =18
PV of savings =4358
Fv or savings required at end of 18 years =50335
FV-PV*(1+r)^n =PMT*((1+r)^n-1)/r)
50335-4358*(1+9%)^18 =PMT*((1+9%)^18-1)/9%)
29777.7892 =PMT*41.301338
PMT =29777.7892/41.301338 =720.99

Amount of savings =720.99

b) Rate =9%
Number of Years =18
FV or savings required at end of 18 years =50335
FV =PMT*((1+9%)^18-1)/9%)
50335 =PMT*41.301338
PMT =50335/41.301338 =1218.73
Amount of savings =1218.73

c) PV =50335
Number of withdrawals =4
Rate =9%
amount of withdrawal =PV/((1-(1+r)^-n)/r) =50335/((1-(1+9%)^-4)/9% =15536.84