The Time Value of Money concept explains that money in our possession today holds more value than money in the future. This is due to the potential interest we can earn on that money; hence, receiving it sooner is more advantageous.
The concept of the time value of money is relevant in key areas of finance and economics, including inflation, the stock market, EMIs, and more.
During our school days, we learned about calculating compound interest in math.
Amount = Principal X (1 + Rate) ^ Time
Compounding involves earning interest on the interest, resulting in exponential growth.
If we take the Amount as future value and the Principal as Present Value, we get:
Future Value = Present Value X (1+ rate of return for each compounding period) ^ number of compounding periods
FV = PV (1+r)^n
Where
FV= Future Value
PV= Present Value
r = rate of return for each compounding period
n = number of compounding periods
If you understand simple algebra, if we were to calculate PV, we can calculate that as:
PV = FV/(1+r)^n
Where
FV= Future Value
PV= Present Value
r = rate of return for each compounding period
n = number of compounding periods
The fundamental concepts of the time value of money are Present Value and Future Value.
Let’s see this using an example if you plan to receive a sum of Rs 1,00,00 at the end of 5 years. What is the present value (today)? Assuming an interest rate of 7 per cent p.a.
PV = FV/(1+r)^n
PV = 100000/(1+7%)^5
PV = 71,298
Similarly, if you have Rs 1,00,000 today and investing for the next 5 years. What will the future value be? Assuming an interest rate of 7 per cent p.a.
FV = PV (1+r)^n
FV = 100000 X (1+7%)^5
FV = Rs 140,225
The future value represents what something is worth at some point in the future.
Both the above calculations can be performed using Excel.
Rate is the annual rate of return.
Nper is the number of periods.
Type refers to when the principal is invested. At the start of the period or end of the period. For simplicity, we can assume the end of the period, which is the assumption built into Excel as well.
Pmt stands for period payment, we will discuss this later.
Rate of return (r)
The rate of return represents the percentage earned on a specific investment.
The compounded annual growth rate (CAGR) of an investment is the compound interest rate that aligns the end value of the investment with its initial value.PV (1+r)^n = FV
r = (FV/PV)^(1/n)-1
or
CAGR = ((End Value/Beginning Value) ^ (1/n)) – 1
Periodic investments or pay-outs (pmt)
In many instances, investors make regular or periodic payments. A typical scenario is seen in loans, where a consistent Equated Monthly Installment (EMI) is paid to the lender every month.
This can be obtained using Excel using the PMT formula where the inputs will be the following
r = the rate of interest on the loan
Nper = the number of periods for which the loan must be repaid
PV = the value of the loan that has to be repaid
NPER
At times, individuals may seek to determine the timeframe for repaying a sum of money, which is referred to in Excel as NPER.
r = rate of interest
PMT = the equal payment
PV = The present value of all the future payments
In today's investment landscape, mutual fund investments are widely favoured, with many opting for systematic investment plans (SIPs).
For instance, if you plan to invest ₹5000 monthly for the next 10 years at an annual interest rate of 12%, you may be curious about the total amount at the end of this period.
Rate = 1% per month (12% p.a./12)
Nper = 120 (10 years x 12)
Pmt = 5000 (monthly)
PV = 0
Type = 0
In Excel you have to type, =FV(1%,120,-5000,0,0)
The value of your SIPs will be ₹11,50,193.45 in ten years.
(outflows are to be shown in negative, while inflows are to be shown as positive. Rs 5k is going out, so shown as negative)
Another common application of these formulas is in calculating EMIs. For example, consider purchasing a house worth Rs 2,00,00,000. If you currently have Rs 50,00,000 and need a loan for the remaining amount, with an assumed 9% annual interest rate and a loan term of 10 years.
Using all this information let's see how you can calculate EMI.
Rate = 0.75% (9% p.a./12)
Nper = 120 (10X12)
Pv = Rs 1,50,00,000 (loan amount 2cr – 50L)
FV = 0
Type = 0
Use Excel and apply PMT formula:
=pmt(0.75%,120,15000000,0,0)
Your monthly EMI is - ₹1,90,013. Since this will be an outflow, the answer is negative.
All these formulas have practical applications in our daily EMI calculations. They are also utilized for more intricate scenarios like determining financial freedom funds or life insurance needs.
“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn't … pays it.” - Albert Einstein
You must train your mind to understand how quickly my capital can double. There is a shortcut to this i.e. 72 divided by the interest rate.
Let's say you are on 7% per annum, your capital will double in 10 years (72 / 7 = 10).
Now imagine if you can grow your capital at 15% p.a., it will take your capital to double in less than 5 years (72 / 15 = 4.80).
Imagine you are 25 years old with a capital of ₹20,00,000. If this capital grows at a rate of 15% per annum, what do you predict your capital will be by the time you reach 60?
Every 5 years your capital doubles.
Age 25, capital is 20L
Age 30, capital will double and become 40L
Age 35, capital will double and become 80L
Age 40, capital will double and become 160L
Age 45, capital will double and become 320L
Age 50, capital will double and become 640L
Age 55, capital will double and become 1280L
Age 60, capital will double and become 2560L
At age 60, your capital will become Rs 25.6 cr. Now you can appreciate why compounding is called the eighth wonder of the world.
A lot of people get the calculation but not the meaning. It is time for you to absorb the true essence of compounding in your life.
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