Use the present value formula to determine the amount to be invested now, or the present value needed. The desired accumulated amount is \( \$ 110,000 \) after 4 years investe \( J \) in an account with \( 2 \% \) interest compounded quarterly. The amount to be invested now, or the present value needed, is \( \$ \) (Round to the nearest cent as needed.)

We start with the present value formula for compound interest \[ PV = \frac{FV}{\left(1+\frac{r}{m}\right)^{m t}}, \] where - \( FV \) is the future value, - \( r \) is the annual interest rate (in decimal form), - \( m \) is the number of compounding periods per year, - \( t \) is the number of years. In this problem: - \( FV = 110\,000 \), - \( r = 0.02 \) (which is \(2\%\)), - Since the interest is compounded quarterly, \( m = 4 \), - \( t = 4 \) years. Substitute these values into the formula: \[ PV = \frac{110\,000}{\left(1+\frac{0.02}{4}\right)^{4 \times 4}}. \] First, calculate \(\frac{0.02}{4}\): \[ \frac{0.02}{4} = 0.005. \] Then, compute the total number of compounding periods: \[ m t = 4 \times 4 = 16. \] Now, the formula becomes: \[ PV = \frac{110\,000}{\left(1.005\right)^{16}}. \] Next, calculate \(\left(1.005\right)^{16}\). Using a calculator, we find \[ \left(1.005\right)^{16} \approx 1.0831. \] Now, determine the present value: \[ PV \approx \frac{110\,000}{1.0831} \approx 101\,514.85. \] Thus, the amount to be invested now is approximately \(\$101,514.85\).