# Calculating future value.

• Jan 3rd 2011, 02:36 PM
nighthawk
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!
• Jan 3rd 2011, 02:39 PM
dwsmith
$\displaystyle \displaystyle\sum_{n=0}^{t}\frac{PMT}{(1+\frac{i}{ k})^n}=PMT\sum_{n=0}^{t}\left(\frac{1}{1+\frac{i}{ k}}\right)^n$

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

$\displaystyle \displaystyle PMT\sum_{n=0}^{t}\left(\frac{1}{1+\frac{i}{k}}\rig ht)^n=\frac{a}{1-r}$
• Jan 3rd 2011, 02:56 PM
nighthawk
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
• Jan 3rd 2011, 02:58 PM
dwsmith
Take a and divide it by 1-r since it is a geometric series.
• Jan 3rd 2011, 03:04 PM
nighthawk
Ok thanks, appreciate the help :)
• Jan 3rd 2011, 03:05 PM
skeeter
you should have a formula to calculate future value in your text or notes ... correct?
• Jan 3rd 2011, 05:04 PM
nighthawk
Thanks for the help guys, and skeeter we have no notes for these problems at all.
• Jan 4th 2011, 04:58 AM
Wilmer
Quote:

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