You invest $10,000 in a fund that will earn 3.2% per year (geometric average). What will be the total value of your investment after 6 years?
The correct answer and explanation is:
To find the total value of an investment after a certain number of years with a given annual geometric average return, you use the formula for compound interest:
Future Value=Present Value×(1+r)t\text{Future Value} = \text{Present Value} \times (1 + r)^t
where
- Present Value is the initial amount invested,
- rr is the annual return rate (expressed as a decimal),
- tt is the number of years.
Given:
- Present Value = $10,000
- Annual return rate, r=3.2%=0.032r = 3.2\% = 0.032
- Time, t=6t = 6 years
Calculating: Future Value=10,000×(1+0.032)6=10,000×(1.032)6\text{Future Value} = 10,000 \times (1 + 0.032)^6 = 10,000 \times (1.032)^6
Using a calculator to find (1.032)6(1.032)^6: (1.032)6≈1.2049(1.032)^6 \approx 1.2049
Now multiply: 10,000×1.2049=12,04910,000 \times 1.2049 = 12,049
So, the total value of the investment after 6 years will be approximately $12,049.
Explanation:
The key concept here is compound interest, where the investment earns interest on both the original principal and the accumulated interest from previous periods. The 3.2% annual geometric average return means the investment grows by about 3.2% each year on average, accounting for compounding effects.
Using the compound interest formula involves raising (1+r)(1 + r) to the power of the number of years. This captures the idea that each year’s growth builds upon the previous year’s total, not just the initial investment.
This growth is exponential rather than linear. If the interest were simple, the increase would be 10,000×0.032×6=1,92010,000 \times 0.032 \times 6 = 1,920, leading to a total of $11,920. However, because of compounding, the actual amount is higher, about $12,049.
Understanding this helps in financial planning and investment decisions, as it demonstrates how money grows over time with compound interest and why starting to invest early can significantly increase the final amount due to the power of compounding.