Think About That - Time Value of Money
$30,000 for a platinum lifetime car wash membership? I don’t think so. Neither does Will Ferrell’s character, James King, in the 2015 film, Get Hard. James is offered this deal by a struggling small business owner, to which he replies:
Well, actually the time value of money is such that if I were to put that same amount in my own fund in 23 years' time, I'd have in excess of $3 million. With that rate of return, I could buy a new car every time it gets dirty.
So, yeah, make the investment.
In the world of finance, one concept stands out as a fundamental truth: the Time Value of Money (TVM). This principle dictates that a sum of money has different values depending on when it is received or paid. In simpler terms, a dollar today is worth more than a dollar tomorrow. We’ll explore why the Time Value of Money is so crucial in our financial decisions.
The Basics of Time Value of Money
The Time Value of Money is based on the idea that money can earn interest or investment returns over time. Therefore, money available now is more valuable because it has the potential to grow. There are several key components to TVM:
The formula for calculating the Future Value of money is:
𝐹𝑉=𝑃𝑉×(1+𝑟/𝑛)𝑛𝑡
This formula shows how present value grows over time with a given interest rate and compounding frequency. Conversely, the Present Value formula, which determines how much a future sum is worth today, is:
𝑃𝑉=𝐹𝑉/(1+𝑟/𝑛)𝑛𝑡
To understand the Time Value of Money, let's consider some everyday examples:
Saving for a Concert
Imagine we're Beyonce fans and she's announced a world tour happening in two years. We plan to save $500 for the concert tickets. If we invest our money in a savings account with a 5% annual interest rate, compounded annually, how much will we have by the time the tickets go on sale?
Using the FV formula:
𝐹𝑉=500×(1+0.05/1)1×2
𝐹𝑉=500×(1.05)2
𝐹𝑉=500×1.1025
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𝐹𝑉=551.25
So, our $500 will grow to $551.25 in two years, thanks to the interest earned.
Financial Planning
Understanding TVM is crucial for making informed financial decisions. Whether we're saving for retirement, planning a major purchase, or investing in our future, knowing how money grows over time helps us make better choices.
Let's say we aim to retire in 30 years and want to have $1 million saved up. If we start investing now with an expected annual return of 6%, how much do we need to invest each year to reach our goal?
Using the Present Value of an Annuity formula:
𝑃𝑉=𝑃𝑀𝑇×(1-(1+𝑟)-𝑛/𝑟)
Rearranging to find the annual payment (PMT):
𝑃𝑀𝑇=𝑃𝑉/(1-(1+𝑟)-𝑛/𝑟)
𝑃𝑀𝑇=1,000,000/(1-(1+0.06)-300.06)
𝑃𝑀𝑇=1,000,000/(1−0.17410.06)
𝑃𝑀𝑇=1,000,000/13.7648
𝑃𝑀𝑇=72,644
We would need to invest approximately $72,644 annually to reach our $1 million goal in 30 years at a 6% return rate.
If we take this principle forward, it’s easy to see why Jay-Z and Beyonce would take a mortgage when purchasing their $88M Bel-Air home. The power moguls certainly could pay all cash for the property, but instead they choose to secure a $52.8M mortgage from Goldman Sachs. Why? They know the time value of money! Even though the mortgage has an interest rate of 3.4%, their cash invested today makes more than the interest payment and more quickly builds equity.
By understanding the time value of money, we set the stage for smarter financial decisions and a more secure financial future. Next time an incredible offer comes our way, we’ll be sure to think about how to leverage our money to maximize the lifetime impact of those funds.
So, Think About That – How can we leverage the Time Value of Money in our financial planning? What steps can we take today to ensure a prosperous future?