# You want to accumulate $1,000,000 in retirement funds by your 65th birthday. Today is your 30th... ## Question: You want to accumulate$1,000,000 in retirement funds by your 65th birthday. Today is your 30th birthday, and you plan on making annual investments into a mutual fund that you project will earn a 9% annual rate of return. Your first deposit will take place today and your last deposit will take place on your 65th birthday. What is the amount of the annual payment you must make each year in order to have $1,000,000 in your account on the day you make your last deposit - that is, on your 65th birthday? ## 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 