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 ​$5,300 at the end of each year into a Roth IRA for the next 42 years. If you earn 6 percent compounded annually on your​ investment, how much will you have when you retire in 42 ​years? How much will you have if you wait 10 years before beginning to save and only make 32 payments into your retirement​ account?

a. How much will you have when you retire in 42 years? (round to nearest cent)

b. How much will you have if you wait 10 years before beginning to save and only make 32 payments into your retirement account? (round to nearest cent)

Answer 1

Annual Payment = 5,300 | Rate = 6%

a) Time = 42 years

To calculate the amount at the end of 42 years, we will use Future Value of Annuity formula.

FV of Annuity = (PMT / R)*((1+R)^T - 1)

Amount after 42 years = (5,300 / 6%)*((1+6%)⁴² - 1)

Amount after 42 years = 88,333.333 * (1.06⁴² - 1) = $ 932,537.89

Hence, the amount at the time of retirement after 42 years is $ 932,537.89

b) Time = 32 years

FV of Annuity = (PMT / R)*((1+R)^T - 1)

Amount after 32 payments = (5,300 / 6%)*((1+6%)³² - 1)

Amount after 32 payments = 88,333.333 * (1.06³²- 1) = $ 481,715.82

Hence, amount at the time of retirement after waiting for 10 years and making 32 payments is $ 481,715.82