Compound Interest ApplicationCompound interest is given by the formula A = P ( 1 + r ) t . Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r , expressed as a decimal.Wyatt is investing money into a savings account that pays 2% interest compounded annually, and plans to leave it there for 15 years. Determine what Wyatt needs to deposit now in order to have a balance of $40,000 in his savings account after 15 years.Wyatt will have to invest $___________ now in order to have a balance of $40,000 in his savings account after 15 years. Round your answer UP to the nearest dollar.

Answer:$29,721Step-by-step explanation:We have been given that Wyatt is investing money into a savings account that pays 2% interest compounded annually, and plans to leave it there for 15 years. We are asked to find the amount deposited by Wyatt in order to have a balance of $40,000 in his savings account after 15 years.We will use compound interest formula to solve our given problem.[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,A = Final amount after T years,P = Principal amount,r = Annual interest rate in decimal form,n = Number of times interest is compounded per year,T = Time in years.Let us convert our given interest rate in decimal form.[tex]2\%=\frac{2}{100}=0.02[/tex]Upon substituting our given values in compound interest formula, we will get:[tex]\$40,000=P(1+\frac{0.02}{1})^{1*15}[/tex][tex]\$40,000=P(1+0.02)^{15}[/tex][tex]\$40,000=P(1.02)^{15}[/tex][tex]\$40,000=P\times 1.3458683383241296[/tex]Switch sides:[tex]P\times 1.3458683383241296=\$40,000[/tex][tex]\frac{P\times 1.3458683383241296}{ 1.3458683383241296}=\frac{\$40,000}{1.3458683383241296}[/tex][tex]P=\$29,720.5891995[/tex]Upon rounding our answer to nearest dollar, we will get:[tex]P\approx \$29,721[/tex]Therefore, Wyatt will have to invest $29,721 now in order to have a balance of $40,000 in his savings account after 15 years.