Answer to Question #246794 in Financial Math for Surendra Singh

Question

A traditional individual retirement account (IRA) is a special type of retirement account in which the money you invest is exempt from income taxes until you withdraw it. If you deposit $100 each month into an IRA earning 6% interest, how much will you have in the account after 20 years?

Answer 1

The monthly deposit $d= \$100$

6% annual rate $r=0.06$

12 months in 1 year $k=12$

We want the amount after 20 years $N=20$

Putting this into the equation:

$P_{20}=\frac{100 ( ( 1 +\frac{ 0.06}{ 12} )^{20 ( 12 )} − 1 )} {(\frac{ 0.06}{ 12} )}$

$P_{20} =\frac{ 100 ( ( 1.005 )^{ 240} − 1 )} {( 0.005 )}$

$P_{20} =\frac{ 100 ( 3.310 − 1 )} {( 0.005 )}$

$P_{20} =\frac{ 100 ( 2.310 )} {( 0.005 )}$

$P_{20}=\$ 46200$

Professor P’s method:

We know the following: PMT=100, i=0.06/12=0.005, n=12(20)=240

$F V =\frac{ P M T ( ( 1 + 0.005 )^{ 240} − 1 )} {( 0.005 )}=\$46,204.09$

The account will grow to $46,200 after 20 years.

Notice that you deposited into the account a total of $24,000 ($100 a month for 240 months). The difference between what you end up with and how much you put in is the interest earned.

In this case it is $46,204.09 – $24,000 = $22,204.09.