An investment grows at 10% annually. If $5,000 is invested, how much is the investment worth after 3 years (compounded annually)? - RTA
Investing 10% Annually: How $5,000 Grows Over 3 Years with Compound Interest
Investing 10% Annually: How $5,000 Grows Over 3 Years with Compound Interest
Investing is a powerful way to build wealth over time—and one of the most motivating factors is compound interest. When an investment grows at a steady rate, even small sums can multiply significantly. Take the example of investing $5,000 at a 10% annual return compounded annually. But how much will your investment be worth after three years?
The Magic of Compound Interest
Understanding the Context
Compound interest means that not only does your original investment grow, but the interest earned also begins to earn interest each year. This simple concept fuels exponential growth over time—especially with annual compounding.
The Calculation: $5,000 Growing at 10% for 3 Years
To calculate the future value of an investment with compound interest, the formula is:
\[
FV = PV \ imes (1 + r)^n
\]
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Key Insights
Where:
- \(FV\) = Future Value (the amount after interest)
- \(PV\) = Present Value (initial investment) = $5,000
- \(r\) = Annual interest rate = 10% = 0.10
- \(n\) = Number of years = 3
Plugging in the values:
\[
FV = 5000 \ imes (1 + 0.10)^3 = 5000 \ imes (1.10)^3
\]
Calculate \(1.10^3\):
\[
1.10^3 = 1.331
\]
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Then:
\[
FV = 5000 \ imes 1.331 = 6,655
\]
So, After 3 Years, Your $5,000 Investment Grows To $6,655
This demonstrates the powerful effect of compounding:
- After Year 1: $5,000 × 1.10 = $5,500
- After Year 2: $5,500 × 1.10 = $6,050
- After Year 3: $6,050 × 1.10 = $6,655
Final Takeaway
An investment of $5,000 growing at 10% annually compounds beautifully: after 3 years, it becomes $6,655. The key takeaway?
- Even modest returns add up quickly when compounded annually.
- Starting early and reinvesting gains maximize long-term growth.
Start now. Even a small investment, combined with steady compound growth, can unlock substantial wealth.
If you’re considering long-term investing, use the compound interest formula to project future returns and stay motivated by seeing tangible growth over time. Your future self will thank you!
