The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A is the new amount
P is the initial amount
r is the rate in decimal
n is the number of the period per year
t is the time in years
Since the new amount is $5000, then
A = 5000
Since the time is 10 years, then
t = 10
Since the interest is 6% compounded monthly, then
n = 12
r = 6/100 = 0.06
Substitute them in the rule to find P
[tex]\begin{gathered} 5000=P(1+\frac{0.06}{12})^{(12)(10)} \\ 5000=P(1.005)^{120} \end{gathered}[/tex]
Divide both sides by (1.005)^120 to find P
[tex]\begin{gathered} \frac{5000}{(1.005)^{120}}=P \\ P=2748.163667 \end{gathered}[/tex]
We need to deposit $2748.16 to the nearest hundredth
