# The company you work for will deposit $150 at the end of each month into your retirement fund....

## Question:

The company you work for will deposit $150 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 25 years from now and estimate that you will need to withdraw $2000 per month during retirement, which will last 30 years. If the account pays 12% compounded monthly, how much do you need to put into the account each month, in addition to your company's deposit, in order to meet your retirement needs?

## Time Value of Money:

The concept behind the time value of money proposes that money can grow over time if used as an investment. This means that a dollar invested today is worth more than a dollar after a certain span of time. The growth of the value of money invested is due to the interest earned on that investment, which is computed using the market rate of interest.

## Answer and Explanation: 1

The problem requires the use of both the present value and future value concepts in finance. Also, since the equal payments are made over equal intervals, we have to use the annuity formula:

*PV* of annuity = *P* x (1 - (1 + *i*)^-*n*) / *i*

*FV* of annuity = *P* x (1 + *i*)^*n* - 1) / *i*

where:

*P* = Periodic payment

*i* = interest rate

*n* = number of periods

According to the problem statement, you want to withdraw $2000 per month during retirement, which will last 30 years. In order for you to withdraw $2000 per month for 30 years, you need to compute how much money you should have in your retirement fund at the start of your retirement (25 years from now). This requires you to compute the present value of $2000 per month for 30 years. Using the formula for the *PV* of the annuity:

*P* = $2000 per month

*i* = 12% / 12 months = 1% per month

*n* = 30 years x 12 months per year = 360 months

*PV* of annuity = $2000 x (1 - (1 + 1%)^-360) / 1%

*PV* of annuity = $194,936.66 --> This is the amount that you need to have in your retirement fund when you reach your retirement age.

Remember, you will retire 25 years from now. This means that, in today's perspective, $194,936.66 is the future amount (that is, 25 years from now).

Now, use the *FV* of annuity formula to compute for the periodic payments needed in order to raise the amount of $194,936.66 after 25 years. Thus:

*FV* of annuity = $194,936.66

*P* = ?

*i* = 12% / 12 months = 1% per month

*n* = 25 years x 12 months per year = 300 months

*FV* of annuity = P x ((1 + *i*)^n) - 1)) / *i*

$194,936.66 = *P* x ((1 + 1%)^300)) - 1) / 1%

P = $103.75

Thus, $103.75 is the amount needed to be deposited in the retirement fund every month. However, since your employer will deposit $150, you don't need to add another deposit in order to meet your retirement needs.

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Chapter 11 / Lesson 2Study the time value of money formula. Learn the time value of money definition and practice how to calculate time value of money to understand the relation to purchasing power.

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