Question

Assume that you contribute $300 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $500 per month for 20 years. Given a 9 percent interest rate, what is the value of your retirement plan after 45 years

Answer 1

To calculate the value of your retirement plan after 45 years, add the value of the contributions made for the first 25 years and the value of the contributions made for the next 20 years. The total value of the retirement plan is $1,143,213.50.

Step-by-step explanation:

To calculate the value of your retirement plan after 45 years, we can break it down into two parts. First, calculate the value of the contributions you made for the first 25 years:

$300 x 12 months x 25 years = $90,000

Using the compound interest formula, the value of these contributions after 25 years at a 9% interest rate would be:

$90,000 x (1 + 0.09)^25 = $609,270.02

Next, calculate the value of the contributions you made for the next 20 years:

$500 x 12 months x 20 years = $120,000

Using the compound interest formula, the value of these contributions after 20 years at a 9% interest rate would be:

$120,000 x (1 + 0.09)^20 = $533,943.48

Finally, add the two values together to find the total value of your retirement plan after 45 years:

$609,270.02 + $533,943.48 = $1,143,213.50

Answer 2

Total FV= $2,555,406.98

Step-by-step explanation:

Giving the following information:

Investment 1:

Monthly deposit= $300

Number of months= 12*45= 540

Interest rate= 0.09/21= 0.0075

Investment 2:

Monthly deposit= $500

Number of months= 12*20= 240

Interest rate= 0.09/21= 0.0075

To calculate the future value, we need to use the following formula on each investment. I separated into two to simplify calculations.

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

A= monthly deposit

Investment 1:

FV= {300*[(1.0075^540) - 1]} / 0.0075

FV= $2,221,463.54

Investment 2:

FV= {500*[(1.0075^240) - 1]} / 0.0075

FV= $333,943.44

Total FV= $2,555,406.98