Ayoung couple wants to have a college fund that will pay $35,000 at the end of each half-year for 8 years. (a) if they can invest at 7%, compounded semiannually, how much do they need to invest at the end of each 6-month period for the next 18 years to begin making their college withdrawals 6 months after their last investment? (round your answer to the nearest cent.)

$6,046.40

Explanation:

First, find the PV of the $35,000 withdrawals annuity at the time of last investment(end of 18 years). This can be solved with a financial calculator using the following inputs;

Recurring semiannual withdrawals; PMT = 35,000

Total duration of withdrawals; N = 8*2 = 16

Semiannual Interest rate; I/Y = 7%/2 = 3.5%

One time cashflows ; FV = 0

Compute present value; PV(at yr18) =  $423,294.088

Next , use the $423,294.088 as your FV goal at the end of year 18.

Future value at yr18; FV = $423,294.088

Total duration of deposits; N = 18*2 = 36

Semiannual Interest rate; I/Y = 7%/2 = 3.5%

One time cashflows ; PV = 0

Compute recurring payment; PMT =  6,046.402

Therefore, they need to invest $6,046.40 at the end of each 6-month period.