Let $P = the amount that Rose placed into the savings account.
The annual compounding rate is r = 5.13% = 0.0513.
The duration is n = 6 years.
The target amount is A = $24,388.
Use the formula
[tex]A=P(1+ \frac{r}{n} )^{nt}
[/tex]
The value of the account after 6 years is
[tex]A=P(1+ \frac{0.0513}{12} )^{12\times6}=P(1.00428^{72})=1.3595P[/tex]
Therefore,
1.3595P = 24388
P = $17,938.95
