You deposit $2,500 into a savings plan at the end of every three months. The interest rate is 5.5% compounded quarterly. Find the value of the annuity after 8 years. Do not round until the final answer. Then, round to the nearest cent.

Question

tkhunny · Answer

P = 2500
i = 0.055
j = i/4
r = 1+j

The last deposit will be just P, with no interest.
The second to last deposit will be Pr, just one quarter's interest.
The third to last deposit will be Pr^2, two quarter's interest.
etc.

All payments, accumulated together $P + Pr + Pr^{2} + ... + Pr^{31}$.  That's 32 total deposits, right?

We can rephrase to $P(1 + r + r^{2} + ... + r^{31}) = P\dfrac{1 - r^{32}}{1-r}$

anonymous · Answer

Thank you so much for this!

anonymous · Answer

just so I can really understand this, If we rephrase it to P$$P \frac{ 1-r^{32} }{ 1-r } $$ then does that mean I would just plug in $$P \frac{ 1-1.013 }{ 1-1.013 }$$           ?????

anonymous · Answer

$$p \frac{ 0.54 }{ 0.013 } =41.53$$

tkhunny · Answer

??
$r = 0.01375$ -- You chopped off WAY too many decimal places.

$r^{32} = 1.5480598641$

$\dfrac{1-r^{32}}{1-r} = 39.8588992$

Rule of thumb: We're talking about 10s of thousands, here.  Use at least 6 decimal places.

$\log_{10}(10000) = 4$.  Add two (2) more for pennies, rather than dollars.  Six (6) is the minimum.