Assume that you contribute $200 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $300 per month for another 30 years. Given a 7 percent interest rate, what is the value of your retirement plan after the 50 years

Total FV= $1,220,441.33

Explanation:

First, we need to calculate the value of the $200 for 20 years. To calculate the future value, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

A= 200

n= 20*12= 240

Intertest rate= 0.07/12= 0.005833

FV= {200*[(1.005833^240) - 1]} / 0.005833

FV= $104,180.27

Now, the value of the $300 for 30 years. At the same time, the future amount of the first investment. Each one with its separate formula.  

$300 monthly investment:

n= 300*12= 360

FV= {300*[(1.005833^360) - 1]} / 0.005833

FV= $365,962.41

$104,180.27 investment:

FV= PV*(1+i)^n

FV= 104,180.27*(1.005833^360)

FV= $854,478,92

Finally, the total FV:

Total FV= 854,478.92 + 365,962.41

Total FV= $1,220,441.33