Question

 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 ​$5,700 at the end of each year into a Roth IRA for the next 41 years. If you earn 9 percent compounded annually on your​ investment, how much will you have when you retire in 41 ​years? How much will you have if you wait 10 years before beginning to save and only make 31 payments into your retirement​ account? How much will you have when you retire in 41 ​years?

Answer 1

Answer:

Investment at the end of each year = $5,700

No. of Years = 41 Years

Rate of interest for compound annually = 9%

To calculate the value at the end of 41 years we need to use the below formula

Future value = Each year Investment * Compound value of an annuity of $1 @9%

= $5,700 *$369.29 (using Compound Value Interest factor of Annuity (CVIFA) table)

= $2,104,953

So, I will have $2,104,953 when I retire in 41 years

In the second situation, the investment is same but after 10 years of waiting

Investment at the end of each year = $5,700

No. of Years = 31 Years

Rate of interest for compound annually = 9%

To calculate the value at the end of 31 years we need to use the below formula

Future value = Each year Investment * Compound value of an annuity of $1 @9%

= $5,700 *$149.58 (using Compound Value Interest factor of Annuity (CVIFA) table)

= $852,606

So, in the second scenario, I will have $852,606 when I retire after 41 years