a 529 plan is a college - savings plan that allows relatives to invest money to pay for a childs future…

a 529 plan is a college - savings plan that allows relatives to invest money to pay for a childs future college tuition; the account grows tax - free. lily wants to set up a 529 account for her new granddaughter and wants the account to grow to $39,000 over 16 years. she believes the account will earn 4% compounded monthly. to the nearest dollar, how much will lily need to invest in the account now? a(t)=p(1 + \\frac{r}{n})^{nt}. lily needs to invest $

a 529 plan is a college - savings plan that allows relatives to invest money to pay for a childs future college tuition; the account grows tax - free. lily wants to set up a 529 account for her new granddaughter and wants the account to grow to $39,000 over 16 years. she believes the account will earn 4% compounded monthly. to the nearest dollar, how much will lily need to invest in the account now? a(t)=p(1 + \\frac{r}{n})^{nt}. lily needs to invest $

Answer

Explanation:

Step1: Identify the values given

$A(t) = 39000$, $r=0.04$, $n = 12$ (monthly compounding), $t = 16$.

Step2: Rearrange the compound - interest formula for $P$

The compound - interest formula is $A(t)=P(1 +\frac{r}{n})^{nt}$. Rearranging for $P$ gives $P=\frac{A(t)}{(1+\frac{r}{n})^{nt}}$.

Step3: Substitute the values into the formula

$P=\frac{39000}{(1+\frac{0.04}{12})^{12\times16}}$. First, calculate the value inside the parentheses: $1+\frac{0.04}{12}=1+\frac{1}{300}=\frac{301}{300}$. Then, calculate the exponent: $12\times16 = 192$. So, $P=\frac{39000}{(\frac{301}{300})^{192}}$. $(\frac{301}{300})^{192}\approx1.8979$. $P=\frac{39000}{1.8979}\approx20550$.

Answer:

$20550$