(b) If the parent decides instead to deposit a lump sum now in order to attain the goal of 100,000 in 10 years, how much must be deposited now? Round your answer to two decimal places.

Here's how to calculate the lump sum deposit needed:<br /><br />**Understanding Compound Interest**<br /><br />The formula for compound interest is:<br /><br />A = P(1 + r/n)^(nt)<br /><br />Where:<br /><br />* A = the future value of the investment/loan, including interest<br />* P = the principal investment amount (the initial deposit or loan amount)<br />* r = the annual interest rate (decimal)<br />* n = the number of times that interest is compounded per year<br />* t = the number of years the money is invested or borrowed for<br /><br />**Solving for P (Present Value)**<br /><br />We want to find P, so we rearrange the formula:<br /><br />P = A / (1 + r/n)^(nt)<br /><br />**Applying the Information**<br /><br />We're given:<br /><br />* A = $100,000 (the desired future value)<br />* t = 10 years<br />* r = 6% = 0.06 (convert percentage to decimal)<br />* n = 12 (compounded monthly)<br /><br />**Calculation**<br /><br />P = $100,000 / (1 + 0.06/12)^(12*10)<br />P = $100,000 / (1 + 0.005)^120<br />P = $100,000 / (1.005)^120<br />P = $100,000 / 1.819396734<br />P ≈ $54,978.16<br /><br />**Answer**<br /><br />The parent must deposit approximately $\boxed{54,978.16}$ now.<br />