We will have the following:
*First: We have the expression:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here "A" is the final amount, "P" is the intitial principal balance, "r" is the interest rate, "n" is the number of times interest applied per time period & "t" is the number of time periods.
*Second: We determine the values given:
A = $30 000
r = 0.1
n = 4
t = 15
*Third: We replace in the expression and solve for P:
[tex]30000=P(1+\frac{0.1}{4})^{(4)(15)}\Rightarrow30000=P(\frac{41}{40})^{(60)}[/tex][tex]\Rightarrow P=\frac{30000}{(\frac{41}{40})^{(60)}}\Rightarrow P=6818.507636\ldots[/tex][tex]\Rightarrow P\approx6818.5[/tex]So, Ann and Tom would need to deposit approximately $6818.5 at the begining.
