Respuesta :
Answer:
$62959
Step-by-step explanation:
We have been given that Parents wish to have 90000 available for a child's education. The child is now 6 years old. We are asked to find the amount of money that parents must set aside at 3% compounded semiannually to meet their financial goal when the child is 18.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
t = Time in years.
[tex]r=3\%=\frac{3}{100}=0.03[/tex]
[tex]n=2[/tex]
[tex]t=18-6=12[/tex]
[tex]A=90000[/tex]
[tex]90000=P(1+\frac{0.03}{2})^{2\times 12}[/tex]
[tex]90000=P(1+0.015)^{24}[/tex]
[tex]90000=P(1.015)^{24}[/tex]
[tex]90000=P(1.4295028119290251)[/tex]
[tex]P=\frac{90000}{1.4295028119290251}[/tex]
[tex]P=62958.952755\approx 62959[/tex]
Therefore, an amount of $62959 must be set aside to meet their financial goal when the child is 18.
