# You want to accumulate $1,000,000 in retirement funds by your 65th birthday. Today is your 30th...

## Question:

## Future value of annuity due:

The future value of annuity due is the compounded value of equal periodic payments that allow an investor to reach a specified target amount in a given year. It differs from ordinary annuity in that the first payment is invested right away.

## Answer and Explanation: 1

Future value of annuity due can be expressed as:

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

Future value (FV) = $1,000,000

Payment (P) = ?

r (rate) = 9.00% or 0.09

n (periods) = 36 ( First deposit is at 30th birthday and the last deposit is at 65th birthday)

{eq}FV=(1+0.09) \times P [ \frac{(1+0.09)^{36}-1}{0.09} ] {/eq}

{eq}P = $4,235.05 {/eq}

Hence the annual payments shall be $4,235.05

#### Learn more about this topic:

from

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.