1. ## Calculating future value.

Hello, i stumbled across these two problems and wasn't entirely sure on how to do it, help is appreciated.

Find the future value FV accumulated in an annuity after investing periodic payments R for t years at an annual interest rate r, with payments made and interest credited k times per year.

1. R=$300, r=6%, t=12, k=4 2. R=$610, r=6.5%, t=25, k=12

Any help is appreciated, thanks!

2. $\displaystyle\sum_{n=0}^{t}\frac{PMT}{(1+\frac{i}{ k})^n}=PMT\sum_{n=0}^{t}\left(\frac{1}{1+\frac{i}{ k}}\right)^n$

$\displaystyle r=\frac{1}{1+\frac{i}{k}}<1 \ \mbox{and} \ a=PMT$

$\displaystyle PMT\sum_{n=0}^{t}\left(\frac{1}{1+\frac{i}{k}}\rig ht)^n=\frac{a}{1-r}$

3. Hey thank for the reply, but, can you explain this better in words? I'm only 16 and i'm having trouble in my pre-calculus class. Thanks

4. Take a and divide it by 1-r since it is a geometric series.

5. Ok thanks, appreciate the help

6. you should have a formula to calculate future value in your text or notes ... correct?

7. Thanks for the help guys, and skeeter we have no notes for these problems at all.

8. Originally Posted by nighthawk
Find the future value FV accumulated in an annuity after investing periodic payments R for t years at an annual interest rate r, with payments made and interest credited k times per year.

1. R=\$300, r=6%, t=12, k=4
There's various ways of "writing down" a financial formula for annuities; one is:

i = r / (100k)
n = t * k

FV = R[(1 + i)^n - 1] / i ; for above: 300(1.015^48 - 1) / .015 = ~20,689.57