bearing in mind the compounding is weekly on an APR, so the compounding cycle is 52, since there are 52 weeks in a year
however, the maturity term in years, is just 50/52, since is 50weeks from 52 in a year, so is 50/52 years, which is just a fraction of a year
[tex]\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\to &\$7,880\\
P=\textit{original amount deposited}\\
r=rate\to 2.938\%\to \frac{2.938}{100}\to &0.02938\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{weekly, thus fifty two}
\end{array}\to &52\\
t=years\to \frac{50}{52}\to &\frac{25}{26}
\end{cases}
\\\\\\
7880=P\left(1+\frac{0.02938}{52}\right)^{52\cdot \frac{25}{26}}[/tex]
solve for P
