# Math Help - savings, interest, inflation etc...

1. ## savings, interest, inflation etc...

Hi

this is the parameters i want to use:

Initial investment (a)

deposit per f1 (d) for example 1000 per month

frequency of deposit per year (f1), f1=12 if it is per month

frequency of compound (f2)

interest or growth per year (g)

inflation(i)

years (n)

I would like to find the formula where you can answer the question:

you start with a one time initial investment (i) of 5000$and then you add 1000$ (d) per month (f) for 8 years (n).

the growth or interest is 7% (g) per year (f2) and the inflation 3%.

the calculations are similar to this one, but also includes initial investment.

interest - Wolfram|Alpha

I've come up with an easier version, not including initial investment or f2 (it only works for annual compounding of g).

It looks like this:

(d(1+((g-i)/f)^(fn)-1)/((g-i)/f)

this one is a bit simplified though. I dont know how to do it. ive been looking around for instance here:
Time value of money - Wikipedia, the free encyclopedia

/TT

2. Originally Posted by Lobotomy
(d(1+((g-i)/f)^(fn)-1)/((g-i)/f)
You need to convert the interest rate such that when compounded at a
frequency equal to the payments frequency, the result is the same as
the "quoted rate frequency"...quite a mouthful, I know!
EXAMPLE: on a monthly payment loan, if the rate is quoted as 12% compounded
semiannually, then a rate compounded monthly needs to be calculated in order to
make it "fit" the formula.

Using g as the quoted annual rate compounding semiannually and h as the "monthly" rate:
(1 + h/12)^12 = (1 + g/2)^2 ; do the math to get:
h = 12[(1 + g/2)^(1/6) - 1]

With g = 12% : h = 12[(1 + .12/2)^(1/6) - 1] = .1171055... (or 11.71%).

In other words, charging interest 12 times per year at 11.71% is the same
as charging interest 2 times per year at 12%.

With your formula, I suggest you replace (g-i) with k,
where k = h - i and h = as above.

Treat the initial investment (call it A) separately:
A(1 + k/12)^(fn)

Hope I was clear enough; not too easy to explain without chalkboard