Future Value Unlocked:
How Today’s Investments Shape Tomorrow’s Wealth
Future Value (FV) is a financial concept that predicts how much an investment today will grow by a specific point in the future, based on a certain interest rate. For individuals and companies alike, FV is instrumental in long-term planning, from saving for college or a house to evaluating which business projects to fund. When we talk about growing wealth, FV is one of the foundational concepts in understanding how present decisions affect future financial standing.
In other words, Future Value tells you how much an investment you make today will be worth in the future.
The Math Behind Future Value
Future Value reveals the impact of compound interest, a concept that allows an initial investment to grow not only on the principal amount but also on the accumulated interest. The general formula for FV is:
FV = PV(1+r)^n
Where:
- PV is the principal amount (initial investment).
- r is the interest rate.
- n is the number of times the interest is compounded.
Future Value and Compounding
Future Value is based on the concept of compound interest – an investment will earn interest over time – and as that interest is earned, it is added to the principle amount (so the investment grows at an exponential rate):
This means that we need to know the periods that we are compounding, and the interest rate for that period.
Typically savings accounts and other interest rates are published as an annual rate – say, 5%. But the interest might compound more frequently than that – often monthly. This means for our future value formula, we need to make sure we are using the same time period for both the interest rate and number of periods.
Example Calculation – Savings Account
Consider Maggie, who invests $2,000 in a savings account offering a 5% annual interest rate, compounded monthly. She plans to keep it there for 3 years and wants to know its future value.
First, we need to get our interest rate and periods the same time scale. Since the savings account compounds monthly, we need to find the monthly interest rate, and the time periods would be how many months she is saving.
Monthly interest rate = Annual interest rate / 12
So for our future value formula, we will use 5%/12 = 0.41667% as the monthly interest rate.
Number of periods = Years x 12 = 36 periods
Now that all of our terms are in the same time scale, we can apply the future value formula:
FV = PV(1 + r) ^n
FV = $2,000(1 + 0.41667%) ^ 36 = $2,323
Utilizing Future Value gives Maggie a much clearer picture of her finances in the future – which can help her more carefully plan out her financial goals.
Example Calculation – Saving for a Car
Let’s relate this concept to a familiar scenario – buying a car. Ryan has been saving up his birthday and holiday gift money since he was a little kid in the hopes of buying his own car when he graduates high school – and successfully saved up $4,000 by the time he turned 14.
He wants to buy a $5,000 car when he turns 18 and wants to know if he will have enough interest growth, or if he needs to keep saving every penny this year too. He just opened a savings account paying 4% interest, compounding monthly. To know if he can just let his money grow, or if he needs to keep saving his cash this year too, he can use the Future Value calculation to see what his bank balance will be in 4 years.
First, his monthly interest rate is 4%/12, and the total periods for his calculation is 4 years * 12 = 48.
Then the Future Value calculation is:
FV = $4,000 ( 1 + 4%/12) ^ 48 = $4,693
Unfortunately, Ryan is going to fall short – he knows he will need to save for another year.
A year later, Ryan successfully saved up another $300 in cash. His savings account also grew (thanks to compound interest) – now his savings balance is $4,163. He deposits his extra $300, making his account total $4,463. Using the future value, he is checking again – does he need to keep saving, or does he finally have enough?
FV = $4,463 x (1 + 4%/12) ^ 36 = $5,031
Perfect – even if he doesn’t save another penny and can be confident he will have enough cash when he turns 18 to afford his car!
Complex Example Calculation – Comparing Investments
Tia just turned 18, with $1,000 in her savings account, which earns 3% a year (compounding monthly). She met with her bank representative to find the best way to make her money grow.
The bank representative gave her three options for what she can do with her money for the next 4 years while she is off studying abroad in college. The options she has available to her are:
- Keep her money in the savings account, which pays 4% per year (compounded monthly).
- She can buy a Certificate of Deposit (CD) that pays 8% (compounded annually) – but the terms specify she can only withdraw once per year – the money is otherwise locked. So her second option is to buy and hold a CD for all 4 years.
- She can also buy that CD (paying 8%, compounding annually) and hold it for just 2 years – then cash it out and put her total earnings back into the regular savings account.
Of course, Tia likes the option of the highest possible interest rate, but she does not like the idea of her money being completely locked up for a long period of time. Tia decides that having her money liquid (or able to be withdrawn and spent at any time) is worth $30 a year, in case she needs it for an emergency.
By using Future Value, she can compare these three investments and decide which is best for her.
Option 1: Savings Account
Her first option is a simple Future Value calculation for what her savings account will be worth in 4 years. Her savings account compounds monthly (so we divide the interest rate by 12), and this will be over 4 years (times 12, so 48 periods).
FV = $1,000 x (1 + 4%/12) ^ 48 = $1,173
Option 2: Long-Term Certificate of Deposit
Her second option is also a simple future value calculation. This time, the compounding is only per year – so we use the annual interest rate, and 4 periods.
FV = $1,000 x (1 + 8%) ^4 = $1,360
But because this locks her money in for 4 years, she subtracts $30/year ($120 total) for her own personal “cost” of not having access to the money.
Final value = $1,360 – $120 = $1,215
Even when she considers the cost of not having access to her money, holding a CD for the entire 4 years looks like the better choice. But what if she wants the best of both worlds – a CD for some time, then cash out to her savings account?
Option 3 – Short-Term Certificate of Deposit
For the third option, she will be investing in a 2-year certificate of deposit, at a 8% interest rate (compounding annually). After that time is up the earned cash will go back into a savings account (earning 4%).
This means we need to make two future value calculations – the time in the CD, then take that value and calculate future value again for the last 2 years in a regular savings account. While the investment is in the CD, it will be earning 6.5% interest
Future Value (CD) = $1,000 x (1 + 8%) ^2 = $1,156
Next, this will go back into the regular savings account, earning 3% interest. We can use the Future Value for this calculation – but since the regular savings account compounds monthly, we use 3%/12 and 2 years times 12 for the interest rate and periods:
Future Value (Savings) = $1,156 (1 + 4%/12) ^ 24 = $1,251
Then, because her savings was locked up for 2 years, she subtracts $30 x 2 = $60:
Adjusted Value = $1,192
Looking at the results, cashing out early and keeping money in her savings account does not look like the best deal – even when she considers that she will have greater access to her cash. The best deal is holding the Certificate of Deposit for all 4 years!
Try It!
Use this Future Value calculator to see how investments grow in the future, with different types of compounding and interest rates!
Future Value Calculator
Result
Conclusion: Unlocking Future Value and Financial Success
Understanding Future Value empowers students like Ryan and Tia to make informed financial decisions, turning theoretical concepts into tangible goals. While the total dollar amount of these examples might seem small, it can mean tens of thousands of dollars to a retirement account or a home purchase in your future!