Basic of Financial Mathematics

Simple Financial Mathematics Tutorial

Time is money; it is actually more than a saying. It is a rule in investment. Time is identical to money and as time flows, money value also increase provide you don’t keep it under your bed. Yes my friend, interest is the things that will make your money grow. Two grands from today obviously more valuable than two grands from ten years in the future, then how will we make our two grand worthwhile? The easiest option is to save your money in a bank. With the knowledge of financial mathematics, you could understand how interests grow your money and could plan your future better. Here are the basic concepts of financial mathematics that you should know.

Future Value Concept

Present value of our money today could be transferred to the equal value in the future. Formula to calculate future value from our investment based on their interest is:

FV = PV * (1 + r)^N

r is the interest rate and N is time period. PV and FV are present value and future value respectively.

Example 1: Let’s take an example of 10% interest per year. If we save two grands today, how much our balance will be on the next year?

FV = PV * (1 + r)^N
FV = 2000 * (1 + 10%)¹ = US$ 2200

Not to tempting huh? Then let’s foresee our balance in ten years

FV = 2200 * (1+10%)¹⁰ = US$ 5187.48

Present Value Concept

Present value concept used to transfers future value to present value. In other word, present value concept used to count how much money we should have now if we want to complete a future payment.

The formula for Present Value is inverted from Future Value formula:

PV = FV/ (1 + r)^N


Example 2: Given an interest rate of 10%, How much will I need as starters to have that US$ 100000 house on the next ten years?

PV = 100000/ (1 + 10%)¹⁰
PV = US$ 38555

The amount of money that we should have now to buy our dream house in the future is

US$ 38555.

Future Value of Annuity

Annuity as a continuous fixed cash flow during certain period. Value that will come from annuities is the real sum of money after few periods from now.

Example 3: if you save ten grands per year for twenty years, how much will you gain after the given time?
For short, the formula to count your future money after years of saving is:

FVA = {A * [(1 + r)ⁿ - 1] / r}

A is annuity, r is the interest rate and n is the given period. So if you save ten grands every years, after 20 years your money will be

{10000 * [(1 + 0.1)²⁰ - 1] / 0.1} = US$ 572,749.99,

That is a lot of money my friend, 20 years of regular savings definitely worth it.

Present Value of Annuity

Present value of annuity is a direct inverse from future value of annuity. PVA is useful to calculate different cash flow in your finance to decide which one is better.
PVA can also be considered how the amount you must invest today at a specific interest rate so that when you withdraw an equal amount each period, the original principal and all accumulated interest will be completely exhausted at the end of the annuity.

Example 4: given 10% interest rate compounded annually, how much should we save today if we want to withdraw $5,000 from our account every year for 10 years?
Formula for present value of annuity is:

PVA = A * {1 – [1 / (1 + r)ⁿ ]} / r

The right answer for the example is
A = 5000
r = 10% = 0.1
n = 10
PVA = 5000 * {1 – [1 / (1 + 0.1)¹⁰]} / 0.1
PVA = $30,723