We are going to employ the future value formula to solve the problem.
The future value, FV, is given as:
[tex]\begin{gathered} FV=PMT(\frac{(1+i)^n-1}{i}) \\ FV\colon\text{Future value} \\ \text{PMT:Periodic payment} \\ i\colon\text{ Interest rate per period} \\ n\colon total\text{ number of payments} \end{gathered}[/tex]From the question, we have the following information:
[tex]\begin{gathered} FV\colon\text{ \$67,000} \\ i\colon\frac{2.55\text{\%}}{52}=\frac{0.0255}{52}=0.0004904 \\ n=52\times17=884 \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} 67,000=\text{PMT(}\frac{(1+0.0004904)^{884}-1)}{0.0004904}) \\ 67,000=\text{PMT(}\frac{(1.0004904)^{884}-1}{0.0004904}) \\ 67,000=\text{PMT(}\frac{1.5425-1}{0.0004904}) \\ 67,000=\text{PMT(}\frac{0.5425}{0.0004904}) \\ 67,000=\text{PMT}(1,106.248) \\ \frac{67,000}{1,106.248}=\text{PMT} \\ \text{PMT}=\text{ \$60.56} \end{gathered}[/tex]Hence, the regular deposit amount is $60.56
