Chapter 4.2, Problem 46AYU

Future Value of Money Suppose that you make deposits of $500 at the beginning of every year into an Individual Retirement Account (IRA), earning interest r (expressed as a decimal). At the beginning of the first year, the value of the account will be $\$500;$ at the beginning of the second year, the value of the account, will be

$\$500+\$500r+\$500=500r+1000$

Verify that the value of the account at the beginning of the third year is $T\left(r\right)=500r^2+1500r+1500$.

The account value at the beginning of the fourth year is $F\left(r\right)=500r^3+2000r^2+3000r+2000$. If the annual rate of interest is $5\%=0.05,$ what will be the value of the account at the beginning of the fourth year?