## Time Value of Money (Part 1 – PMT)

### The Background

Back in 2005, some time after I started my first job the thought of owing a car started coming in mind.

Question was how do I start planning for the same and where do I start from?

After finalizing the budget (and also the color ) of the car to be bought and the time frame by when I will buy it, question was “How can I afford the car without a loan?” Yes, I didn’t want to take debt on me for something which was guying to be a liability.

Similar questions came in mind anytime I was planning to buy an asset such as a home, plan for the higher education for kids, planning for a vacation abroad, or even when planning for the retirement. Though at those times, I did think or plan of taking loan due to the various amounts involved. Nevertheless, the questions remained.

- How much I need to Save?
- How much can I Save?
- How do I save That Much?

I wish I knew basics of Personal Finance Management at that time. Thankfully, I now know.

### Getting the Basics Right

Let’s start with the same question of the car.

**Q. If I want to buy a car in 5 years whose current cost is Rs.5,00,000. How much money should I save every year?**

- Option 1 – Save 1 Lakh Every Year
- Option 2 -Save Increasing Sums of money
- Option 3 -Save Decreasing Sums of money

If I have to save **Decreasing Sums of Money**, I am having to put aside a big amount in the beginning itself and if I can afford to cut out that amount this year, I should be able to cut out the same amount next year as well. And the year after. Which means I can basically afford a bigger car. (Where is this going? I already decided the budget keeping all these factors in mind)

If I have to save **Increasing Sums of Money**, I am having to put aside a big amounts later in the years. I don’t know whether my salary will increase or my business will grow by that %. Future is anyways at the best uncertain so I would like to have certain degree of certainty.

**Saving constant amounts **every year seems like the most sensible over as it gives me a certainty I was looking for. (A reason why EMI’s – Equated Monthly Installments are most popular ).

But, will the amount that I save bear no **INTEREST**? Which means that 1Lakh that I am saving will actually be –**1 Lakh + Interest** **= Amount more than 1Lakh**

**Interest**ing observation. Of course it will – whether you keep it in savings account, a fixed deposit or even invest in bonds (given it will be short term investment).

So, what do I do now.? How much should I then save if not 1 Lakh?

This is where **Time Value of Money **comes in Handy. Let’s have a look.

### Time Value of Money – Basics

We need to keep 5 things in mind when we talk about Time Value of Money. These are –

- Present Value (PV)
- Future Value (FV)
- Rate (I/Yr)
- Periods (Nper or N)
- Periodic Payments (PMT)

#### Calculating Regular Payments (PMT)

Lets try to understand what these values are and how can they be of our help by once again revisiting the above example.

**Q. If I want to buy a car in 5 years whose current cost is Rs.5,00,000. How much money should I save every year?**

Money at Hand which can be termed as Present Value of my corpus was at that point Nil. Hence, **PV = 0**

I want to accumulate a total of 5 Lakh, hence the Future value of my money, **FV = 5,00,000**

The time horizon for me is 5 Years, hence period, **N = 0**

Let’s assume that while accumulating the money, I try to invest it where it can be safe, secure and also generate decent returns for me, Bonds or Mutual Fund’s Debt funds are good option and I can expect around 8% annual returns on my investment. So the Rate of Return, **I/Yr = 8%**.

I now need to calculate the regular amounts that I need to save each year which essentially means calculating **PMT**

Now we need to open an excel and perform the following tasks.

PV | 0 |

FV | 500000 |

N | 5 |

I/Yr | 8% |

PMT | ??? |

Now, in the PMT formula, type =PMT(8%,5,0,500000,1) and hit enter. You will see the value of PMT coming as **-78,915**.

PV | 0 |

FV | 500000 |

N | 5 |

I/Yr | 8% |

PMT | ₹ -78,915 |

Now the value is coming as Negative. What does this signify?

When we perform financial calculations, any amount, coming to our pocket is termed as a Positive value and any amount leaving our pocked is denoted by Negative sign. In the above case, it signifies that the amount 78,915 will have to be paid from our pocket every year.

The same can be verified in the table below as well.

Installment | Previous Year Amount | Total (A+B) | Rate | Interest Amount | NETT |
---|---|---|---|---|---|

78915 | 8% | 6313 | 85228 | ||

78915 | 85228 | 164143 | 8% | 13131 | 177275 |

78915 | 177275 | 256190 | 8% | 20495 | 276685 |

78915 | 276685 | 355600 | 8% | 28447 | 384048 |

78915 | 384048 | 462963 | 8% | 37037 | 500000 |

So, we see that by saving 78915 every year at an assumed rate of 8% annual return, we will be able to save 5 Lakh in 5 Years. ?

#### Calculating Regular Payments (PMT) when we have some PV

In the above example, let’s assume I had 1 Lakh with me. Now I need to accumulate 4 Lakh for the total amount to be 5 Lakh at the end of 5 Years. Thus, in this case our PV will become 1 Lakh and the revised values will look something like the table below. Notice the – sign in front of PV amount. This is the amount going out from my pocket, hence a negative sign.

PV | -100000 |

FV | 500000 |

N | 5 |

I | 8% |

PMT | ₹ -55,725 |

The value of PMT in this case gets reduced to 55,725.

By changing various values of PV, FV, I and N, we can find the value of regular payments that are required to be done or regular savings to be made.

What do you think will the payment be required if I have to save the same amount in 4 years on time instead of 5 years at an 8% assumed rate of annual returns and with initial amount being Zero. Let me know the answer in comments.

## Summary – but a Doubt as well.

So, today we learnt how you can calculate regular payments which are required to achieve a Future Value. These type of calculations are very common when we are saving money for a future goal or also in cases where we are giving regular payments against a sum of money taken. We will learn more about PMT in a different post to understand few more nuisances about it.

The doubt we had was, that while I was saving for my Car, I completely ignored one aspect – Its True future value. Given that as time progresses, things become costlier, will the car still be available for 5 Lakh after 5 years?

How will inflation impact the value of car that I am planning to buy?

Will the 5 Lakh that I am depositing now be sufficient for me to fund the car? We will have a look at this and some other aspects in our next blog post. Till then – **Bachate Rahein, Kamate Rahein** because **EveryPaisaMatters**

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