Answer
\[\$13,175.19\]
Work Step by Step
Calculation of principal amount of deposit can be done with the mentioned formula:
\[P=\frac{A}{{{\left( 1+\frac{r}{n} \right)}^{nt}}}\]
Where A denotes the Future value of the loan, P denotes the Principal amount, R denotes the rate of interest, t denotes the number of years and n denotes the number of times compounding is done in a year.
Compute the principal amount by substituting the values in the formula as mentioned below:
\[\begin{align}
& P=\frac{A}{{{\left( 1+\frac{r}{n} \right)}^{nt}}} \\
& =\frac{\$75,000}{{{\left(1+\frac{0.05}{4}\right)}^{4\times35}}}\end{align}\]
Solve and simplify the equation as follows:
\[\begin{align}
& P=\frac{\$75,000}{{{\left(1+0.0125\right)}^{140}}}\\&=\frac{\$75,000}{{{\left(1.0125\right)}^{140}}}\\&=\frac{\$75,000}{5.692519}\\&=\$13,175.19\end{align}\]
Hence, the amount deposited for the retirement is \[\$13,175.19\]
