# Saving for college in 20 years, a father wants to accumulate $40,000 to pay for his daughter's college expenses. If he can 6% interest, compounded quarterly, how much must he invest now to achieve his goal? Ava-May Nelson 2020-10-26 Answered Saving for college in 20 years, a father wants to accumulate$40,000 to pay for his daughters
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Clara Reese
If P dollars are deposited in an account eqarning interest at an annual rate r, compounded n times each year, the amount A in the account after t years is given by
$A=P{\left(1+\frac{r}{n}\right)}^{nt}$
A=\$40,000
r=6%=0.06
$t=20$ years
$n=4$(Compounded quarterly)
Thus,
$40000=P{\left(1+\frac{0.06}{4}\right)}^{4\left(20\right)}$
$40000=P{\left(1+0.015\right)}^{80}$
$40000=P{\left(1.015\right)}^{80}$
$40000=P\left(3.2906\right)$
Divide both sides by 3.2906
$P=12155.61$
Final statement:
The initial deposit is $\mathrm{}12155.61$.
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