In order to find the deposit Leory needs to make, let's use the following formula for compound interest:
[tex]C=A\cdot(1+\frac{i}{n})^{nt}[/tex]Where C is the final value, A is the initial value, i is the interest rate, t is the time and n is a constant related to the period of interest.
For this case, we have C = 1000, i = 10% = 0.1, n = 12 (the interest is compounded monthly), and t = 3, so we have that:
[tex]\begin{gathered} 1000=A(1+\frac{0.1}{12})^{12\cdot3} \\ 1000=A(1+0.008333)^{36} \\ 1000=A(1.008333)^{36} \\ 1000=A\cdot1.34818 \\ A=\frac{1000}{1.34818}=741.74 \end{gathered}[/tex]So the initial deposit is $741.74.
