Future Value of money Formula How to Calculate with Example

The future value of money is essential to be able to answer questions like, “What is the present worth of a real estate investment I’m going to make in the future?”

In this, we can find what the investment is worth today, then after taking into account inflation, we can estimate the worth in future.

In 15 years’ time, what will be the worth of Rs.20,590,353/-?

In order to answer this query, the opportunity cost must be ascertained. For present or future worth problems, the opportunity cost will remain consistent.

Therefore, the chance to incur this cost is 9%.

To determine the future value of money, we must compound the amount with the rate of opportunity cost.

Remember the compounding formula we discussed in the preceding chapter –

P*(1+R)^(n) yields the future value.

Future value = P*(1+R)^(n)

Where,

P = Amount

R = opportunity cost

N = Time period

Applying this,

= 20,590,353 * (1+9%)^(15)

Before I reveal the answer, what does your gut feeling tell you it might be?

We need to do the opposite when calculating the future value of 20,590,353 at 9% for 15 years. We should expect that the answer is Rs.75,000,000/-, since we have already established this figure with present value calculation. To double-check our maths, let’s put it to the test!

= 20,590,353 * (1+9%)^(15)

= 75,000,000

This is the worth of money in the future.

Essentially, if you were offered 75,000,000 after 15 years or 20,590,353 today, both of these amount to the same thing.

– The offer

Remember, the start of the chapter? We started with an example, if a generous friend gives 2 options:

Option A- He provides you with an immediate sum of Rs.10,000/-.

Option B- He guarantees to provide you with Rs.10,000/- precisely in two years’ time.

It’s likely that you chose option B, but how can we make this situation even better now that we understand the concept of the time value of money? There is surely a way to improve it.

Here, we need to assess the worth of Rs.10,000/- today and its estimated value over the next two years.

If we pick option A, this money can be invested in an interest bearing instrument and expand the amount. Currently, a two year fixed deposit yields approximately 7.5%, so we need to calculate the future value of Rs.10,000/- if it is compounded at 7.5%.

= 10000*(1+7.5%)^(2)

= Rs.11,556.25/-

If we choose option B, we would be taking a value significantly lower than Rs.10,000/-. A fairer gesture would be either Rs.10,000/- right away or Rs.11,556.25/- after two years!

One of the fundamental principles in finance is that money available now is more valuable than money in the future. This is because it can be invested and grow at a risk-free rate, offering a greater return.

– Real-life applications

To finish this chapter, let us take a look at some realistic scenarios and use the concepts of Future Value (FV) and Present Value (PV). These are fictitious, but the importance of applying FV and PV will be more evident in later parts of this module.

Question– Let’s assume a situation. With your daughter currently being ten and the expected US university enrollment in fifteen years, it is wise to start saving for her tuition fee of Rs.6,500,000/-. How much should you have today so as not to be overwhelmed by the amount due closer to the date?

Answer – To assess the situation, it’s essential to determine whether it is a present or a future value case. That might not be clear at first, so a bit more comprehension is necessary. One simple solution is to study the numbers involved.

It is obvious that our cash needs will amount to Rs.6,500,000/- in 15 years’ time, so it is essential to plan ahead.

We can use the present value formula we just learned to calculate how much we need to save today in order to meet our current cash requirement.

Present value = Future value / (1+ discount rate ) ^ (time)

The 7.5%, 15 year Government bond serves as an apt proxy for the discount rate, so we will use it.

Present value =  6,500,000/(1+7.5%)^(15)

= Rs.21,96,779/-

By investing Rs.21,96,779/- today, we can achieve our goal of having the target funds within 15 years.

For those of you who are looking to save for their kid’s future schooling, this module focuses on providing insight into the concept of present value. Although this may be a way to amass a fund for it, there are other alternatives available.

Let us utilise an example of the future value of money to conclude this chapter. You may be familiar with this scenario –

Your dad’s friend at the workplace is an enterprising wheeler-dealer who frequently advertises money-making schemes. He stopped by to have a cup of tea and, while he was there, tried to get your family to invest a substantial amount of money. According to him, an investment of Rs.200,000 today would yield a reward of Rs.450,000 in just 15 years’ time.

Will you accept this offer?

Answer:

This is a difficult problem that requires the application of the future value concept. Fortunately, it’s relatively easy to understand –

Investment required today – Rs.200,000/-

Expected value from this investment – Rs.450,000/-

Taking into account the 7.5% opportunity cost and Rs.200,000/-, we must decide if this investment is worthwhile. We’ll use extrapolation to calculate the answer.

Future value = 200000*(1+7.5%)^15

= Rs. 591,775.5

Compare this to the Rs.450,000/- and this deal is no longer viable. You will have to politely ask your dad to refuse the offer.

Consider this: how could you use the idea of the present value of money to address this dilemma?