Personal Finance Math

One of the reasons I have been good at personal finance decisions is that I am very comfortable with using math. While being good at math is not necessary, it's important to have a good understanding a few math concepts to be good at personal finance. Compound interest and Loan Amortization are the two I feel are most important. If one can master these two math concepts, over 80% of personal finance concepts will become intuitive:

First, here a few variable definitions:

i = interest (daily, monthly, or yearly, depending on the period n)
n = number periods (days, months or years)
P = principal ( amount of money loaned)
M = monthly payment since most loans are paid monthly.
FV - future value
PV - present value (amount in savings)

Compound Interest

FV = PV * (1 + i)^n

This formula is useful for calculating:

1. How much one's savings will be worth n years in the future



2. The impact of inflation after n years

The table below shows examples of using this equation to calculate savings growth and inflation impact. Savings 1 shows the growth of a $100 at 2 % interest per year for 10 years and savings 2 shows the growth at 5% per year. Inflation 1 shows the decline of $100 at 2% inflation after 10 years and inflation 2 shows the reduction at 5% per year.

	Value at n = 10 years
Calculation	FV	PV	i
Savings 1	$121.90	$100	2%
Savings 2	$162.89	$100	5%
Inflation 1	$100	$82.03	2%
Inflation 2	$100	$61.31	5%

Loan Amortization

M = P * i / (1- (1/(1+i)^n)

This formula is used to calculate:

1. Monthly payments for a home mortgage.



2. How much more one pays for something with an installment loan.

This formula is especially useful for determining how changes interest and time affects one monthly payments and total payment. Not surprisingly, a higher interest rate results in a higher monthly and total payment. However, while a shorter time (n) results in a higher monthly payment, the total payments are much lower. Also, the different between Total Payments and the principal (P) is the total amount of interest paid.

	Monthly Payment Equation
M	P	i	n	Total Payments
$790.91	$100,000	5%	180	$142,342.85
$898.93	$100,000	7%	180	$161,789.09
$536.82	$100,000	5%	360	$193,255.78
$665.30	$100,000	7%	360	$239,508.90

Using these equations have been very helpful to me for deciding to save early, choosing a good mortgage deal, and avoiding debt.

For more on The Practice of Personal Finance , check back every Thursday for a new segment.

This is not financial advice. Please consult a professional advisor.

Copyright © 2007 Achievement Catalyst, LLC