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 formula of the future value of an annuity ordinary is
Fv=pmt [((1+r)^(n)-1)÷r]
Fv future value?
PMT yearly payment 1200
R interest rate 0.07
N time 49 years (70-21)

Fv=1,200×(((1+0.07)^(49)−1)÷(0.07))
Fv=454,798.80

Hope it helps!

Answer 2

The amount of money the person will have is $\fbox{\begin\\\ \bf \ 454,800\\\end{minispace}}$.

Further explanation:

In the question it is given that the amount of money invested per month is $\ 100$.

So, the total amount of money invested in $1$ year or $12$ months is calculated as follows:

$\fbox{\begin\\\ 100\times 12=1200\\\end{minispace}}$

This implies that the total amount of money invested in $1$ year is $\ 1200$.

Amount of money invested grows at a rate of $7\%$ per year.

A person started investing the money at an age of $21$ years and decided to withdraw the money at the age of $70$ years.

So, the total time for which the money was invested is calculated as follows:

$\fbox{\begin\\\ 70-21=49\\\end{minispace}}$

The formula to obtain the future value of the invested money is as follows:

$\fbox{\begin\\\ FV=PV\left[\dfrac{(1+r)^{t}-1}{r}\right]\\\end{minispace}}$

Substitute $1200$ for $PV$, $0.07$ for $r$ and $49$ for $t$ in the above equation.

$\begin{aligned}FV&=1200\left[\dfrac{(1+0.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{(1.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{26.53}{0.07}\right]\\&=1200\times379\\&=454800\end{aligned}$

Therefore, the future value of the invested money is $\ 454,800$.

Thus, the amount of money the person will have is $\fbox{\begin\\\ \bf \ 454,800\\\end{minispace}}$.

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Answer details:

Grade: College

Subject: Mathematics

Topic: Time value of money

Keywords: Future value, present value, interest, time period, investment, money, 7 percent, $100, amount, invested money, formula.