Question

# Charles estimated a minimum need of \$229,000 for college education...

Charles estimated a minimum need of \$229,000 for college education fund for his son in 13 years when his son will start college. Assume that after-tax rate of return that Charles is able to earn from his investment is 8.32 percent compounded annually. Charles has already earmarked \$17,165 for his son education. He understands that this amount is not enough to finance his son education. He is going to invest additional amounts each year at the beginning of the year until his son starts college. Compute the annual beginning of-the-year payment that is necessary to fund the current deficit. (Please use annual compounding, not simplifying average calculations).

Round the answer to two decimal places. Solved by verified expert

Annual beginning of year payment to fund the current deficit = \$7,590.98

Step-by-step explanation

Estimated minimum need in 13 years(Future value) = \$229,000

Number of periods(n) = 13 years

Annual compounding rate(r) = 8.32% = 0.0832

Amount earmarked(set aside now)= \$17,165

Additional amount to invested at the beginning of the year until Charles son starts college(Annuity due) = ?

Annuity due refers to a series of equal payments made at equal intervals at the beginning of the period.

In this case the Future value(\$229,000) will be equal to the future value of the amount earmarked add the future value of the annuity due.

Future value of the amount earmarked = Amount earmarked *(1 + r)n

= \$17,165 * ( 1 + 0.0832)13

= \$17,165 * (1.0832)13

= \$17,165 * 2.826262313

= \$48,512.7926

Future value of annuity due formula = Annuity due* [((1 + r)n - 1) / r] * (1 + r)

= Annuity due * [((1 + 0.0832)13 - 1) / 0.0832] * (1 + 0.0832)

= Annuity due *[(1.083213 - 1) / 0.0832] * 1.0832

= Annuity due * 21.95026819 * 1.0832

= Annuity due * 23.7765305

Future value(\$229,000) will be equal to the future value of the amount earmarked add the future value of the annuity due.

\$229,000 = \$48,512.7926 + Annuity due * 23.7765305

\$229,000 - \$48,512.7926 = Annuity due * 23.7765305

\$180,487.2074 = Annuity due * 23.7765305

\$180,487.2074 / 23.7765305 = Annuity due

\$7,590.981678 = Annuity due

Annual beginning of year payment to fund the current deficit = \$7,590.98