The compound interest formula is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
From the question, the final expected amount is given to be $15,000. The time is 10 years, and the interest rate is 6%. The value of n is 2 for a semi-annual compounding period. Therefore, we have the following parameters:
[tex]\begin{gathered} A=15,000 \\ r=\frac{6}{100}=0.06 \\ n=2 \\ t=10 \end{gathered}[/tex]
Therefore, we can solve as follows:
[tex]\begin{gathered} 15000=P(1+\frac{0.06}{2})^{2\times10} \\ 15000=P(1+0.03)^{20} \\ 15000=P(1.03)^{20} \\ P=\frac{15000}{1.03^{20}} \\ P=8305.14 \end{gathered}[/tex]
Given the cost of the purchase to be $8,305.14, we can share this among the three of them. Therefore, each of them will contribute:
[tex]\Rightarrow\frac{8305.14}{3}=2768.38[/tex]
Each of them will contribute $2,768.38.
