Question

If a person starts investing $100 per month starting at age 21, and that money earns a 7% return every year, how much will this person have when turning 70 years old? for ease of calculation, assume starting balance of $0 and annual contributions of $1,200 (12*$100).

Answer 1

The future worth of money with the investment made every year can be calculated through the equation,
            F = A x ((1 + r)^n - 1/ (r))
Substituting the known values,
            F = ($1200) x ((1 + 0.07)^49 - 1) / (0.07))
                  F =  $454,798.8 

Hence, the future worth of the made contribution is $454,798.8. 

Answer 2

The person will have $454,798 when he will be 70 years old.

Further Explanation:

Future Value: Future value is the value of a product in the coming future. it is the value of the goods that would be realized after the sales of the goods in the future. It is calculated by using the future value annuity factor. Future value is used for the selection of the project. The value of the project can be accurately ascertained by determining the future value of the product because the product would be sold in the future at the future value.

$\begin{aligned}\text{FV of the annuity}&=\text{P}\left(\dfrac{(1+r)^{n}-1}{r}\right)\\\text{P}&=\text{Periodic Payment}\\r&=\text{rate per period}\\n&=\text{number of periods}\end{aligned}$

Calculate the Future Value:

$\begin{aligned}\text{FV of the annuity}&=\text{P}\left(\dfrac{(1+r)^{n}-1}{r}\right)\\&=\ 1,200\left(\dfrac{(1+0.07)^{49}-1}{0.07}\right)\\&=\ 1,200\times 378.99\\&=\ 454,798\end{aligned}$

Therefore, the person will have $454,798 when he will be 70 years old.

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Answer details:

Grade: High School

Subject: Time Value of money

Chapter: Financial Management

Keywords: If, a person, starts, investing, $100, per, month, starting, at age 21, and, that, money, earns, a 7%, return, every, year, how, much, will, this, person, have, when, turning, 70, years, old,  for, ease, of, calculation, annual, contributions, of present value.