Question

Irene plans to retire on January 1, 2020. She has been preparing to retire by making annual deposits, starting on January 1, 1980, of 2400 dollars into an account that pays an effective rate of interest of 8.3 percent. She has continued this practice every year through January 1, 2001. Her goal is to have 1.4 million dollars saved up at the time of her retirement. How large should her annual deposits be (from January 1, 2002 until January 1, 2020) so that she can reach her goal?

Answer 1

Let the annual deposits be x
2400/8.3%*(1.083^22-1)*1.083^19+x/8.3%*(1.083^19-1)=1.4*10^6
=>x=(1.4*10^6-2400/8.3%*(1.083^22-1)*1.083^19)*8.3%/(1.083^19-1)
=>x=18039.1700