Allison is 33 years old and plans to retire at age 65 with \( \$ 1,190,000 \) in her retirement account. What amount would she have to set aside now in an investment paying \( 7 \% \) annual interest if the compounding is done daily (assume 365 days in a year)? The amount to be invested now is \( \$ \square \). (Round to the nearest cent as needed.)

To calculate how much Allison needs to invest now to accumulate \( \$1,190,000 \) by age 65 with a 7% annual interest rate compounded daily, we can use the formula for present value: \[ PV = \frac{FV}{(1 + \frac{r}{n})^{nt}} \] Where: - \( PV \) = present value (the amount to be invested now) - \( FV \) = future value (\$1,190,000) - \( r \) = annual interest rate (0.07) - \( n \) = number of times interest is compounded per year (365) - \( t \) = number of years until retirement (65 - 33 = 32) Now we can plug in the values: \[ PV = \frac{1,190,000}{(1 + \frac{0.07}{365})^{365 \times 32}} \] Calculating \( (1 + \frac{0.07}{365})^{365 \times 32} \) gives us approximately \( 7.134 \). Then: \[ PV = \frac{1,190,000}{7.134} \approx 166,800.55 \] So, the amount Allison needs to invest now is approximately \( \$166,800.55 \).