Question

you are planning for your child's education. you would like to make deposits every 26 weeks (half year) in years 0 through 21, with your first deposit to be made today (a total of 43 deposits), so that your child may make withdrawals in each of the years 18 through 21 for tuition. tuition is currently $2,900/year, and is expected to grow at 4% for each of the next 10 years, and then at 5% for each of years 11 through 21. you can earn a nominal annual rate of 8.632%, with interest compounded weekly (52-week year) in a college savings account. how much must you deposit every 26 weeks?

Answer 1

To calculate the deposit amount, use the formula for the future value of an annuity with compound interest. By plugging in the given information, you can determine the amount you need to deposit every 26 weeks.

To calculate the amount you need to deposit every 26 weeks, you can use the formula for future value of an annuity with compound interest. The formula is:

PV = PMT × (1 - (1 + r/n)^(-nt)) / (r/n)

where PV is the present value (deposit amount per period), PMT is the payment amount per period, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, you would be solving for PMT.

Using the given information:

Total number of deposits (t) = 43

Total number of withdrawals (t) = 4 (from years 18 to 21)

Interest rate (r) = 8.632% compounded weekly

Deposit frequency (n) = 26 weeks (half year)

Withdrawal frequency (n) = 1 year

Tuition cost (PMT) = $2,900/year, with 4% growth for the first 10 years and 5% growth for the next 11 years.