Mark deposits $700 each month in a retirement plan paying 6% compounded monthly. How much will he have in the account after 24 years

Question

john_es · Answer

You should use the formula for compund interest,
$$C=C_0\left(1+\frac{r}{100}\right)^n$$
Where C_0 is the initial capital, r is the mensual rate in % and n is the time in months.

tkhunny · Answer

Build it!!!!

i = 0.06 -- Annual interest rate to be compounded monthly.
j = i/12 = 0.005 -- Monthly interest rate
r = 1 + j = 1.005 -- Monthly Accumulation factor

Now, just write ti down.

700(r + r^2 + r^3 + ... + r^(24*12)) = $700\dfrac{r-r^{289}}{1-r}$

john_es · Answer

Yes, a geometric progression is funnier to build.

anonymous · Answer

im getting 831.99 and its wrong

tkhunny · Answer

How did you get that?  john_ES's formula is good for a single deposit.  I built a complete formula.  Please demonstrate your intermediate results.

$r^{289}\;=\;??$

anonymous · Answer

Find the amount of the annuity if the deposit is $500 quarterly for 6 years at 7% compounded quarterly.

tkhunny · Answer

This is the EXACT same problem.  There is no difference in the solution.

Note: You really have to specify WHEN the payment is made.  Beginning?  End?  Middle?  Spread?  What?

anonymous · Answer

That's the whole question.. there is nothing more to it....

tkhunny · Answer

I understand that, but it requires assumptions.  Insist that there are better questions.  They are often missing pieces.  Very annoying.