# You have determined that you will need $3,000,000 when you retire in 40 years. You plan to set...

## Question:

You have determined that you will need $3,000,000 when you retire in 40 years. You plan to set aside a series of payments each year in an account yielding 12% per year to reach this goal. You will put the first payment in the account one year from today, and the payments will grow with your income by 3% per year. Calculate your first annual payment into this account. Calculate the last payment. Please solve it step by step with the formula used.

## Future value of annuity:

Future value of annuity is given as the total value of a uniform series of cash flows to be receive or paid at equal periodic intervals, at the end of the series. It is the total compounded value of all the deposits made at the end of the period.

## Answer and Explanation: 1

Future value with growing annuity is given as:

Here,

Future value = $3,000,000.00

*P* = First Annual payment

*r* = Rate = 12% = 0.12

*n* = Number of years = 40

*g* = Growth rate = 0.03

So,

3,000,000 = *P* x ((1.12^40 - 1.03^40) / (0.12 - 0.03))

or,

*P* = 3,000,000 / 997.6548 = $3,007.05

So,

First payment = $3,007.05

Last payment

= First payment x (1 + Growth)^Number of years

= 3,007.05 x 1.03^40

= $9,809.11

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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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