Question

2) An individual contributes $400 per month to a 401(k) retirement account. The account earns interest at a nominal annual interest rate of 6% (APRs 696) with interest being credited yearly, what is the value of the account after 40 years (to the nearest 1,000)? a) $736,000 b) $743,000 c) $797,000 d) $918,000

Answer 1

The interest rate per month is :

  $i = \frac{r}{m}= \frac{0.06}{12}= 0.005$

where;

r denote nominal annual interest rate

m denote  months

Now we calculate uniform series compound amount factor. before that we calculate total numbers of months(n).

$n= \left \langle 40 yr \right \rangle\left [ 12\frac{month}{year} \right ]$

$= 480 months$

$\dpi{120} \bg_white F= A\left \{ \frac{(1+i)^{}{n}-1}{i} \right \}$

$\dpi{120} \bg_white = \$ 400\left \{ \frac{(1+0.005)^{480})-1}{0.005} \right \}$

$\dpi{120} = \$ 796,596 \ Nearest \ to\ \$ 797,000$

Therefore,the value of amount after 40 years is $797,000 (option c).