**What is Time Value of Money**

*“A bird in the hand is worth two in the bush” – Miguel de Cervantes*

The time value of money is one of the most important concepts in finance. Money that is in possession today is more valuable than future payments because today’s money can be invested to earn positive returns in future.The understanding of Time Value of Money leads to better decision making in some of the major financial decisions like — calculating sum assured requirements for your life insurance needs, computing monies which will be required for child education/wedding in future, corpus needed to fund retirement, comparing alternative investment decisions, comparing house lease v/s buy decisions, horrendous impact of carrying credit card debts etc.

**What is time Value?**

Money has time value. The value of Rs. 1 today is more worthy than the value of Rs. 1 tomorrow. This economic principle recognizes that the passage of time affects the value of money. **This relationship between time and money is called the ‘Time Value of Money’.**

If someone owes you Rs 10,000/- , it is advantageous to get the money today If you get this money today:

–> You could earn interest and invest it and you will receive this quantity plus some other amount in the future.

–> You can use it to pay your debts and therefore, lower the interest amount paid on your debt.

–> Or you can spend it and enjoy it as you wish.

**Understanding Present Value , Future Value, Compound Interest, Time and their Relationship:**

A sum of money today is called a **present value (PV). A sum of money at a future time is termed a ****future value (FV). **

**The time period in between the present and future value can be no of years, no of months, no of quarters or any unit of ****period. (n).**

The interest rate or growth rate in which the present value can be employed . This is the **interest rate per period.(i)** The effects of value versus time is best usually described by compound interest. Change in Value over time is impacted by factors like inflation, tax rates , discounting rates etc.

**Future Value**** ****is calculated as follows : Future Value (FV) = Present Value (PV) * (1 + i) ^ n**

Alternatively, given a future value then,

**Present Value**** can be calculated as follows : ****Present Value (PV) = Future Value (FV) / (1 + i) ^ n**

**Compounding **

**Compounding is the mathematical procedure for determining “future value” and is virtually the reverse of discounting**

**Discounting **

Discounting is the mathematical procedure for determining “present value”.

**Some Examples :**

1. If you invest Rs 1,000 today at an interest rate of 10 percent, how much will it grow to be after 5 years?

FV = 1000 * (1 + .1) ^ 5 = Rs 1,610.51

2. If you were given an option to get Rs 1,00,000 , six years hence OR option of receiving Rs 55,000 now. What will you choose.

In this case, you bring down the future value to the present value and then make a decision (or judgement). Let us assume a discounting rate of 12%.

So, PV = 1,00,000 / (1 + .12) ^ 6 = Rs 50,663.11.

Option A Present Value comes to Rs 50,663.11 and Option B is Rs 55,000. And the choice becomes obvious. In this way different rates can be used to make alternative quality decisions and arrive at decisions quantitatively.

3.If you invest Rs 11,000 in a mutual fund today, and it grows to be Rs 50,000 after 8 years, what compounded, annualized rate of return did you earn?

Using the above formula again : FV = PV * (1 + n) ^ i

50000 = 11000 * (1 + n) ^ 8 ; So, n = 20.84 % (Wow!! — This is a good investment)

4.** Rule of 72 (Quick!!! — )**

How long does it take to double Rs 5,000 at a compound rate of 12% per year (approx.)?

Approx years to double = 72/ i% (Cool!!)

In the above case it will be = 72/ 12% = 6 years. (This is rough, Actually it will be 6.12 years)

**Thus, Your ability to measure time value of money can be THE vital difference between your making a good or bad investment decision.**