parents wish to have $100,000 available for a childs education. if the child is now 2 years old, how much…

parents wish to have $100,000 available for a childs education. if the child is now 2 years old, how much money must be set aside at 8% compounded semiannually to meet their financial goal when the child is 18? click the icon to view some finance formulas. the amount that should be set aside is $ (round up to the nearest dollar.)

parents wish to have $100,000 available for a childs education. if the child is now 2 years old, how much money must be set aside at 8% compounded semiannually to meet their financial goal when the child is 18? click the icon to view some finance formulas. the amount that should be set aside is $ (round up to the nearest dollar.)

Answer

Explanation:

Step1: Determine the number of years and compound - periods

The child is 2 years old and the goal is when the child is 18, so the number of years $t=18 - 2=16$ years. Since it is compounded semiannually, the number of compounding periods $n = 2t=2\times16 = 32$, and the interest rate per period $i=\frac{r}{m}$, where the annual interest rate $r = 8%=0.08$ and $m = 2$ (compounded semiannually), so $i=\frac{0.08}{2}=0.04$. The future value $A = 100000$.

Step2: Use the compound - interest formula $A=P(1 + i)^n$ to find the present value $P$

We can rewrite the formula as $P=\frac{A}{(1 + i)^n}$. Substitute $A = 100000$, $i=0.04$, and $n = 32$ into the formula: $P=\frac{100000}{(1 + 0.04)^{32}}$.

Step3: Calculate $(1 + 0.04)^{32}$

$(1 + 0.04)^{32}=e^{32\ln(1.04)}\approx3.508066$.

Step4: Calculate the present value $P$

$P=\frac{100000}{3.508066}\approx28506$.

Answer:

$28506$