Poonam wants to invest in an account today to have 4000 at the end of 8 years. If she can invest at 4.25% compounded semi-annually, how much does she need to invest? A) 2857.24 B) 2055.15 C) 3380.68 D) 2867.16

Here's how to solve this compound interest problem:<br /><br />**Understanding the Formula**<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 />**Applying the Formula**<br /><br />In Poonam's case:<br /><br />* A = $4000 (the desired future value)<br />* r = 4.25% = 0.0425 (as a decimal)<br />* n = 2 (compounded semi-annually means twice a year)<br />* t = 8 years<br />* P = ? (This is what we need to find)<br /><br />We can rearrange the formula to solve for P:<br /><br />P = A / (1 + r/n)^(nt)<br /><br />**Calculations**<br /><br />P = $4000 / (1 + 0.0425/2)^(2*8)<br />P = $4000 / (1 + 0.02125)^16<br />P = $4000 / (1.02125)^16<br />P = $4000 / 1.39615<br />P = $2867.16<br /><br />**Answer:**<br /><br />The correct answer is D) $2867.16<br />