Related to The Business of Life: Saving for Retirement) (Future value of an ordi
ID: 2815507 • Letter: R
Question
Related to The Business of Life: Saving for Retirement) (Future value of an ordinary annuity) You are graduating from college at the end of this semester and after reading the The Business of Life box in this chapter, you have decided to invest $5,100 at the ond of each year into a Roth IRA for the next 44 years. If you earn 8 percent compounded annually on your investment, how much will you have when you retire in 44 years? How much will you have if you wait 10 years before beginning to save and only make 34 payments into your retirement account? How much will you have when you retire in 44 years? (Round to the nearest cent)Explanation / Answer
We can use the future value of ordinary annuity formula to calculate value of at the time of retirement under both option. Option 1 (yearly investment for 44 years) Future value of annuity = P x {[(1+r)^n -1]/r] Future value of annuity = value at the end of 44th year when you retire = ? P = Yearly investment = $5100 r = rate of interest = 8% n = no.of years = 44 Future value of annuity = 5100 x {[(1+0.08)^44 -1]/0.08] Future value of annuity = 5100 x 356.95 Future value of annuity = $18,20,443.19 Value of at time of retirement = $18,20,443.19 Option 2 (yearly investment for 34 years) Future value of annuity = P x {[(1+r)^n -1]/r] Future value of annuity = value at the end of 44th year when you retire = ? P = Yearly investment = $5100 r = rate of interest = 8% n = no.of years = 34 Future value of annuity = 5100 x {[(1+0.08)^34 -1]/0.08] Future value of annuity = 5100 x 158.63 Future value of annuity = $8,08,996.02 Value of at time of retirement = $8,08,996.02