What is the Time value of Money? The Time Value of Money explains that a rupee today is more valuable than a rupee a year. This is because the individual person postpones the consumption by saving for future consumption. There is inflation where a rupee can have greater now than a year after. A rupee can be invested to generate a positive return.
Future Value of Single Amount
Does: The value of money increases or decreases over a given period of time.We are interested in the ability to pay the money today. The time value of money can be calculated using a few formulae. The time value of money is going to be derived from the compound interest formula.
Compound interest = P(1+r/n) ^ nt
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
After 1 year the value of money is reduced.
For example, the amount of 10000 paid every year will have less value.
After 1 year Compound Interest = 10000(1–10/100)power 1 = 10000*90/100= 9000
Money can travel forward and money can travel backward. When money is backward then we call discounting and when money travels forward then we call it compounding. When we move the money to today’s value then we will use discounting. Discounting is the process as it is easier to bring it to today’s value. How long does it take to double 5000 at the compound interest rate of 12% per year (approx)
We can use the rule of 72. So it takes 72/12% = 6 years approx.
First — Future Value or Present Value?
Future Value : Present(Now) -> Future
Present Value : Future Value -> Present(Now)
Second — Single amount or Amount which is a one-time lump sum. Annuity — Paying Cash flow which is the same fixed amount at all fixed intervals of the period. For example EMI for the loan that we pay. So the main requirement of Annuity is an equal amount and equal interval. The concept of Timeline. It says that a timeline allows finding in a sequence of time.
Future Value — We use compounding where what is the value of money at some point in time. For Present Value — We travel from backward. The variable that is involved in TVM is the Interest rate, Time, Principal, Future Value, and Present Value. There are 2 types of annuity. It is a stream or series of equal payments to receive at equal intervals in the future. Ordinary annuties: the payment is received at the end of each period. The second payment will come after 1 year. Annuities due: the payment is made at the beginning of each period.
The following are the formula
Future Value — Single amount. Here is the payment used in lumpsum.
Present Value — Single amount. Here the payment is used in a lump sum.
Future Value — Annuity. Future Value — Annuity in advance. Present Value — Annuity
Doubling Period
The period during which the amount would double at a given rate. There is a rule of 72 which can identify the duration when the amount will be doubled.
Rule of 72 = 72/Interest
There is also Rule of 69 to calculate the doubling formula
Rule of 69 = 0.35 +69/Interest Rate
Shorter Compound Period
Compounding can be done in a short period of time which is less than 1 year. Let us take a previous example of investing an amount of Rupees 1000 where it pays 12% interest semi-annually, so it pays every 6 months.
So Year 1, the Principal calculated using compound interest in the first 6 months is =1000*(1+12%/2)= 1060
So Year 1, the Principal calculated using compound interest in the second 6 months is =1060*(1+12%/2)= 1123.6
So the Principal at the end of Year1 compound annually,
=1000*(1+12%) = 1120.0
Therefore there is a difference between the principal when calculate using compound interest annually and semi-annually.
Effective Versus Nominal Rate
If the nominal interest is compounded semi-annually, then the effective interest rate is higher.
The formula for effective interest rate and nominal rate is as follows.
R = (1+k/m)^m-1
Where r = effective rate of interest
k= nominal rate of interest
m= frequency of compounding per year.
Future Value of an Annuity
What is the Future Value of Annunity ? An Annuity is a series of periodic cashflows(payment or receipts) of equal amounts. For example we pay for insurance payment which is regular annuity amount. When the cash flow is done at the end of each period of annuity then it is called a regular annuity or deferred annuity. When the cash flow occur at the beginning of each period of annuity then it is called annuity due.
The formula for the future value of an annuity is as per the formula.
FVAn = A(1+k)^(n-1) + A(1+k)(n-2)+ ….. + A
= A[((1+k)^n-1)/k]
Where
FVAn = future value of an annuity which has a duration of n periods.
A = constant periodic flow
k = interest rate per period.
n = duration of the annuity
The term ((1+k)^n-1)/k is called (FVIFAk,n) Future Value interest factor for an annuity.
For example, There are 4 annual payments for an amount of Rs 2000 for which there is an interest of 8% per year.
What is the formula of the Future Value spreadsheet in excel? Some of the formula are Present Value(PV), Future Value(FV), equal period payment (PMT), number of periods(NPER), interest/discount rate(RATE). The build-in formal is PMT(RATE, NPER, PV,[FV],[TYPE]). The type is 0 or 1 which means if the payment is done at the end of the period or beginning of each period.
Present Value of a Single Amount
Assuming that an investor is told that he will be paid 3000 after a few years. What will be the present value that I have to deposit once in a single lump sum amount at a given interest rate?
The value to be paid after 3 years is 3000. The interest rate is 10%
The present value of 3 years is 3000
The present value 2 years is 3000((1/(1+10%))(1/(1+10%)0
The present value current year = 1000(1/1.10)(1/1.10)(1/1.10)
The formula for the present value of an annuity for a single amount. In this case, we have to reverse the compounding to make it discounting.
If FV=PV(1+k)^n then for discounting we can make PV=FV(1/(1+k)^n). The value 1/(1+k)^n is called discounting factor or present value interest factor PVIFk,n.