How to Calculate the Future Value of an Investment: A Complete Guide with Formulas and Examples

The Future Value (FV) of an investment tells you how much your money will be worth at a later date, considering a specific rate of return. The formula you use depends on whether the investment earns simple interest or compound interest.

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1. Future Value with Simple Interest

Simple interest is calculated only on the initial principal amount. The formula is:

FV = P (1 + r t)

Where:

• FV = Future Value
• P = Initial principal (the amount you invest)
• r = Annual interest rate (as a decimal)
• t = Number of years

Example:

If you invest $10,000 at an interest rate of 5% per year for 3 years, the future value is:

FV = 10,000 (1 + 0.05 \times 3) = 10,000 (1.15) = 11,500

So after 3 years, your investment grows to $11,500.

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2. Future Value with Compound Interest

Compound interest is calculated on both the principal and accumulated interest. The formula is:

FV = P \left(1 + \frac{r}{n} \right)^{nt}

Where:

• FV = Future Value
• P = Initial principal
• r = Annual interest rate (as a decimal)
• n = Number of times interest is compounded per year
• t = Number of years

Example:

You invest $10,000 at 5% annual interest, compounded quarterly

FV = 10,000 \left(1 + \frac{0.05}{4} \right)^{4 \times 3}

FV = 10,000 \left(1.0125 \right)^{12}

FV \approx 10,000 \times 1.1593 = 11,593

So, after 3 years, your investment is worth $11,593 instead of $11,500, because compounding earns extra interest.

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3. Future Value with Continuous Compounding

When interest compounds infinitely, use the continuous compounding formula:

FV = P e^{rt}

Where ee is Euler’s number (≈ 2.718).

Example:

For the same $10,000 investment at 5% annually, compounded continuously for 3 years:

FV = 10,000 \times e^{(0.05 \times 3)}

FV = 10,000 \times e^{0.15} \approx 10,000 \times 1.1618 = 11,618

So, with continuous compounding, your investment grows to $11,618.

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Comparison of Future Values

Investment Type	Formula	Future Value after 3 years ($10,000 at 5%)
Simple Interest	FV = P (1 + rt)	$11,500
Compound Interest (Quarterly)	FV = P \left(1 + \frac{r}{n} \right)^{nt}	$11,593
Continuous Compounding	FV = P e^{rt}	$11,618

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Key Takeaways:

1. Simple interest is straightforward but earns less over time.
2. Compound interest earns more because it reinvests accumulated interest.
3. Continuous compounding provides the highest growth but only slightly more than frequent compounding.