# You want to have $2,000,000 saved by the time you retire which is in 45 years. You can invest...

## Question:

You want to have $2,000,000 saved by the time you retire which is in 45 years. You can invest your money a portfolio that is estimated to earn 8 percent per year. You have no money saved today but would like to start investing starting at the end of this month. How much do you need to save each month?

## Future Value Annuity:

When a series of periodic payments are made at a regular period, then using future value of annuity, one can determine the worth of the payments at the end of the period or after n periods. Future value annuity could be an ordinary annuity, where the payments are made at the end of the period. On the other hand, when the payments are made at the beginning of the period, future value of annuity due formula is used. It uses the same principle as the time value of money and has the application in various field such as portfolio worth after n periods of payment.

## Answer and Explanation: 1

Using Future Value Annuity formula, payment to be made per month can be calculated as below:

{eq}P = FV*r/ [(1+r)^n - 1] {/eq}

where,

P = payments to be made every month

r = interest rate per month = 8%/12 = 0.67%

n = 45*12 = 540

FV= $2,000,000

Putting the values in the above equation

P = 2000000*0.006667 / [(1+0.006667)^540 - 1]

P = 13333.33 /[36.1636 - 1]

P = $379.18

Answer: A payment of $379.18 needs to be paid each month to save $2,000,000.

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Chapter 21 / Lesson 15An annuity is a type of savings account that pays back the investor in the future. Learn the formula used to calculate an annuity's value, and understand the importance of labeling specific numbers to calculate an output over time.

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