# 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 10% 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?

## Annual Investment:

When an investor accumulates their savings and invests them on a per annum basis, in any form of investment is regarded as an annual investment. Annual recurring deposits and annual mutual fund investments are a few examples.

## Answer and Explanation: 1

Future value of savings = $1,000,000

Time period = 65 -30 = 35 years

Since the first deposit is made now itself i.e., at the 30th birthday itself, 35 years +1 year = 36 years will be the investment period.

Interest rate = 10%

Let *x* be the annual amount to be deposited.

The amount to be deposited each year can be found using the below equation.

{eq}\begin{align*} {\rm\text{Future value of savings}}\, &= \,{\rm\text{Annual amount deposited}}\, \times \left( {\dfrac{{1 - {{\left( {1 + \,{\rm\text{Interest rate}}} \right)}^{{\rm\text{Number of years}}}}}}{{{\rm\text{Interest rate}}}}} \right)\\ \$ 1,000,000\, &= \,x\, \times \left( {\dfrac{{1 - {{\left( {1 + 10\% } \right)}^{36\,{\rm\text{years}}}}}}{{10\% }}} \right)\\ \$ 1,000,000 &= x \times 299.1268\\ x &= \dfrac{{\$ 1,000,000}}{{299.1268}}\\ &= \$ 3,343.06 \end{align*} {/eq}

Thus, the amount to be deposited per annum is **$3,343.06.**

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Chapter 5 / Lesson 16Understand the definition of future value and the future value formula. Explore some examples that show how to calculate the future value of an investment.

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